Calculus — Full Problem Index (1/3)

Problem	Final Answer	Solution
d(ln(x))/d(x)	1/x	Find the Derivative - d/dx natural log of x
(∫_^)(ln(x)*d(x))	x*ln(x)−x+C	Evaluate the Integral
d(e^x)/d(x)	e^x	Find the Derivative - d/dx e^x
(∫_^)(e^(2x)d(x))	(e^(2*x))/2+C	Evaluate the Integral integral of e^(2x) with respect to x
d()/d(x)1/x	−1/(x^2)	Find the Derivative - d/dx 1/x
d(x^2)/d(x)	2*x	Find the Derivative - d/dx x^2
d()/d(x)1/(x^2)	−2/(x^3)	Find the Derivative - d/dx 1/(x^2)
d(sin^2(x))/d(x)	sin(2*x)	Find the Derivative - d/dx sin(x)^2
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative - d/dx sec(x)
(∫_^)(e^x*d(x))	e^x+C	Evaluate the Integral integral of e^x with respect to x
(∫_^)(x^2*d(x))	(x^3)/3+C	Evaluate the Integral integral of x^2 with respect to x
(∫_^)(√(,x)*d(x))	2/3*x^(3/2)+C	Evaluate the Integral
d(cos(x))/d(x)	−2sin(x)cos(x)	Find the Derivative - d/dx cos(x)^2
(∫_^)(1/x*d(x))	ln(x)	Find the Derivative - (1/x) dx
(∫_^)(sin^2(x)*d(x))	x/2−sin(2*x)/4+C	Evaluate the Integral integral of sin(x)^2 with respect to x
d(x^3)/d(x)	3*x^2	Find the Derivative - d/dx x^3
d(sec(x))/d(x)	2sec(x)tan(x)	Find the Derivative - d/dx sec(x)^2
(∫_^)(cos^2(x)*d(x))	x/2+sin(2*x)/4+C	Evaluate the Integral integral of cos(x)^2 with respect to x
(∫_^)(sec^2(x)*d(x))	tan(x)+C	Evaluate the Integral integral of sec(x)^2 with respect to x
d(e^(x^2))/d(x)	2xe^(x^2)	Find the Derivative - d/dx e^(x^2)
(∫_0^1)(√(3,1+7x)d(x))	45/28	Evaluate the Integral
d(sin(2*x))/d(x)	2cos(2x)	Find the Derivative - d/dx sin(2x)
d(tan^2(x))/d(x)	2tan(x)sec^2(x)	Find the Derivative - d/dx tan(x)^2
(∫_^)(1/(x^2)*d(x))	−1/x+C	Evaluate the Integral integral of 1/(x^2) with respect to x
d(2^x)/d(x)	2^x*ln(2)	Find the Derivative - d/dx 2^x
y=ln(a)	ln(a)	Graph natural log of a
d(cos(2*x))/d(x)	−2sin(2x)	Find the Derivative - d/dx cos(2x)
(d(x)*e^x)/d(x)	e^x*(x+1)	Find the Derivative - d/dx xe^x
(∫_^)(2xd(x))	x^2+C	Evaluate the Integral integral of 2x with respect to x
d(ln(x))/d(x)	(2*ln(x))/x	Find the Derivative - d/dx ( natural log of x)^2
d(ln(x^2))/d(x)	2/x	Find the Derivative - d/dx natural log of (x)^2
(d(3)*x^2)/d(x)	6*x	Find the Derivative - d/dx 3x^2
(∫_^)(xe^(2x)*d(x))	1/2xe^(2x)−1/4e^(2*x)+C	Evaluate the Integral integral of xe^(2x) with respect to x
(d(2)*e^x)/d(x)	2*e^x	Find the Derivative - d/dx 2e^x
d(ln(2*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 2x
(d(−)*sin(x))/d(x)	−cos(x)	Find the Derivative - d/dx -sin(x)
d()/d(x)(4x^2−x+5)	8*x−1	Find the Derivative - d/dx 4x^2-x+5
d()/d(x)16√(4,4x^4+4)	(64x^3)/√(4,(4x^4+4)^3)	Find the Derivative - d/dx y=16 fourth root of 4x^4+4
(d(2)*x^2)/d(x)	4*x	Find the Derivative - d/dx 2x^2
(∫_^)(e^(3x)d(x))	(e^(3*x))/3+C	Evaluate the Integral integral of e^(3x) with respect to x
(∫_^)(cos(2x)d(x))	1/2sin(2x)+C	Evaluate the Integral integral of cos(2x) with respect to x
d()/d(x)1/√(,x)	−1/(2*x√(,x))	Find the Derivative - d/dx 1/( square root of x)
(∫_^)(e^(x^2)*d(x))	√(,π)/2*erfi(x)+C	Evaluate the Integral integral of e^(x^2) with respect to x
e^∞	∞	Evaluate e^infinity
d()/d(x)x/2	1/2	Find the Derivative - d/dx x/2
(d(−)*cos(x))/d(x)	sin(x)	Find the Derivative - d/dx -cos(x)
d(sin(3*x))/d(x)	3cos(3x)	Find the Derivative - d/dx sin(3x)
d()/d(x)1/(x^3)	−3/(x^4)	Find the Derivative - d/dx 1/(x^3)
(∫_^)(tan^2(x)*d(x))	tan(x)−x+C	Evaluate the Integral integral of tan(x)^2 with respect to x
(∫_^)(1*d(x))	x+C	Evaluate the Integral integral of 1 with respect to x
d(x^x)/d(x)	x^x*(ln(x)+1)	Find the Derivative - d/dx x^x
d()/d(x)xln(x)	1+ln(x)	Find the Derivative - d/dx x natural log of x
d(x^4)/d(x)	4*x^3	Find the Derivative - d/dx x^4
(lim_x→3)((3*x−5)/(x−3))	Does Not Exist	Evaluate the Limit limit as x approaches 3 of (3x-5)/(x-3)
(∫_^)(x^2ln(x)d(x))	(x^3*ln(x))/3−(x^3)/9+C	Evaluate the Integral
d(√(,x))/d(x)	1/(2√(,x))	Find the Derivative - d/dx f(x) = square root of x
d()/d(x)x^2sin(x)	x^2cos(x)+2x*sin(x)	Find the Derivative - d/dx x^2sin(x)
(∫_^)(sin(2x)d(x))	−1/2cos(2x)+C	Evaluate the Integral integral of sin(2x) with respect to x
(d(3)*e^x)/d(x)	3*e^x	Find the Derivative - d/dx 3e^x
(∫_^)(xe^xd(x))	x*e^x−e^x+C	Evaluate the Integral integral of xe^x with respect to x
d()/d(x)*x^2	2*x	Find the Derivative - d/dx y=x^2
d(√(,x^2+1))/d(x)	x/√(,x^2+1)	Find the Derivative - d/dx square root of x^2+1
d(sin(x^2))/d(x)	2xcos(x^2)	Find the Derivative - d/dx sin(x^2)
(∫_^)(e^(−2x)d(x))	−1/2e^(−2x)+C	Evaluate the Integral integral of e^(-2x) with respect to x
(∫_^)(ln(√(,x))*d(x))	1/2xln(x)−1/2*x+C	Evaluate the Integral
d(e^2)/d(x)	0	Find the Derivative - d/dx e^2
d()/d(x)*(x^2+1)	2*x	Find the Derivative - d/dx x^2+1
(∫_^)(sin(x)*d(x))	−cos(x)+C	Evaluate the Integral integral of sin(x) with respect to x
d(arcsin(x))/d(x)	1/√(,1−x^2)	Find the Derivative - d/dx arcsin(x)
(lim_x→0)(sin(x)/x)	1	Evaluate the Limit limit as x approaches 0 of (sin(x))/x
(∫_^)(e^(−x)*d(x))	−e^(−x)+C	Evaluate the Integral integral of e^(-x) with respect to x
d(x^5)/d(x)	5*x^4	Find the Derivative - d/dx x^5
d()/d(x)2/x	−2/(x^2)	Find the Derivative - d/dx 2/x
d(ln(3*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 3x
d(x^(1/2))/d(x)	1/(2√(,x))	Find the Derivative - d/dx x^(1/2)
d(√(,x))/d(x)	1/(2√(,x))	Find the Derivative - d/d@VAR f(x) = square root of x
d(cos(x^2))/d(x)	−2xsin(x^2)	Find the Derivative - d/dx cos(x^2)
d()/d(x)1/(x^5)	−5/(x^6)	Find the Derivative - d/dx 1/(x^5)
d(√(3,x^2))/d(x)	2/(3√(3,x))	Find the Derivative - d/dx cube root of x^2
(∫_^)(cos(x)*d(x))	sin(x)+C	Evaluate the Integral integral of cos(x) with respect to x
(∫_^)(e^(−x^2)*d(x))	√(,π)/2*erf(x)+C	Evaluate the Integral integral of e^(-x^2) with respect to x
d(x^3)/d(x)	3*x^2	Find the Derivative - d/d@VAR f(x)=x^3
(∫_0^10)(4x^2+7d(x))	4210/3	Evaluate the Integral
(∫_^)((ln(x))^2*d(x))	x(ln(x))^2−2xln(x)+2x+C	Evaluate the Integral
d((log_)(x))/d(x)	1/x	Find the Derivative - d/dx log of x
d(arctan(x))/d(x)	1/(1+x^2)	Find the Derivative - d/dx arctan(x)
d(ln(5*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 5x
(d(5)*e^x)/d(x)	5*e^x	Find the Derivative - d/dx 5e^x
d(cos(3*x))/d(x)	−3sin(3x)	Find the Derivative - d/dx cos(3x)
(∫_^)(x^3*d(x))	(x^4)/4+C	Evaluate the Integral integral of x^3 with respect to x
(∫_^)(x^2e^xd(x))	e^x(x^2−2x+2)+C	Evaluate the Integral integral of x^2e^x with respect to x
d()/d(x)16√(4,4x^4+4)	(16√(,2)*x^3)/((x^4+1)^(3/4))	Find the Derivative - d/dx 16 fourth root of 4x^4+4
d()/d(x)x/(e^x)	(1−x)/(e^x)	Find the Derivative - d/dx x/(e^x)
(lim_x→3)(arctan(e^x))	arctan(e^3)	Evaluate the Limit limit as x approaches 3 of arctan(e^x)
(∫_^)((e^x−e^(−x))/(e^x+e^(−x))*d(x))	ln(e^x+e^(−x))+C	Evaluate the Integral
d(3^x)/d(x)	3^x*ln(3)	Find the Derivative - d/dx 3^x
(∫_^)(xe^(x^2)d(x))	1/2*e^(x^2)+C	Evaluate the Integral integral of xe^(x^2) with respect to x
(d(2)*sin(x))/d(x)	2*cos(x)	Find the Derivative - d/dx 2sin(x)
sec(0)	1	Evaluate sec(0)^2
d(ln(x^2))/d(x)	2/x	Find the Derivative - d/dx natural log of x^2
d(√(,x^3))/d(x)	(3√(,x))/2	Find the Derivative - d/dx square root of x^3
d(e^(−x^2))/d(x)	−2xe^(−x^2)	Find the Derivative - d/dx e^(-x^2)
d()/d(x)1/x	−1/(x^2)	Find the Derivative - d/d@VAR f(x)=1/x
(d(4)*x^2)/d(x)	8*x	Find the Derivative - d/dx 4x^2
(∫_^)(x^(−2)*d(x))	−1/x+C	Evaluate the Integral integral of x^-2 with respect to x
(∫_^)((e^√(,x))/√(,x)*d(x))	2*e^√(,x)+C	Evaluate the Integral
d(5^x)/d(x)	5^x*ln(5)	Find the Derivative - d/dx 5^x
(d(2)*x^3)/d(x)	6*x^2	Find the Derivative - d/dx 2x^3
√(3,x)	x^1/3	Simplify cube root of x
(lim_x→0)(1/x)	Does Not Exist	Evaluate the Limit limit as x approaches 0 of 1/x
d()/d(x)3/(x^2)	−6/(x^3)	Find the Derivative - d/dx 3/(x^2)
d()/d(x)x/(x+1)	1/((x+1)^2)	Find the Derivative - d/dx x/(x+1)
d()/d(x)1/x	−1/(x^2)	Find the Derivative - d/dx f(x)=1/x
d(x^2)/d(x)	2*x	Find the Derivative - d/dx f(x)=x^2
(∫_^)(csc^2(x)*d(x))	−cot(x)+C	Evaluate the Integral integral of csc(x)^2 with respect to x
(∫_^)(e^(−3x)d(x))	−1/3e^(−3x)+C	Evaluate the Integral integral of e^(-3x) with respect to x
d()/d(x)*(1−x^2)	−2*x	Find the Derivative - d/dx 1-x^2
d()/d(x)xsin(x)	x*cos(x)+sin(x)	Find the Derivative - d/dx xsin(x)
d(y^2)/d(y)	2*y	Find the Derivative - d/dy y^2
d(sin(x))/d(x)	3sin(x)cos(x)	Find the Derivative - d/dx sin(x)^3
(∫_0^1)((x^2+1)e^(−x)d(x))	3−6/e	Evaluate the Integral
(∫_^)(1/√(,x)*d(x))	2√(,x)+C	Evaluate the Integral
(∫_^)(te^(−3t)*d(t))	−1/3te^(−3t)−1/9e^(−3*t)+C	Evaluate the Integral integral of te^(-3t) with respect to t
(∫_^)(tan(x)*d(x))	ln(sec(x))	Evaluate the integral of tan(x)dx
(d(5)*x^2)/d(x)	10*x	Find the Derivative - d/dx 5x^2
d(√(,1−x^2))/d(x)	−x/√(,1−x^2)	Find the Derivative - d/dx square root of 1-x^2
d(4^x)/d(x)	4^x*ln(4)	Find the Derivative - d/dx 4^x
d(ln(ln(x)))/d(x)	1/(x*ln(x))	Find the Derivative - d/dx natural log of natural log of x
d(cos(x))/d(x)	−3cos(x)sin(x)	Find the Derivative - d/dx cos(x)^3
d(ln(x^2+1))/d(x)	(2*x)/(x^2+1)	Find the Derivative - d/dx natural log of x^2+1
(∫_^)(−cos(x)*d(x))	−sin(x)+C	Evaluate the Integral integral of -cos(x) with respect to x
(∫_^)(x^(−1)*d(x))	ln(x)	Evaluate the Integral of x^(-1)dx
d(ln(sin(x)))/d(x)	cot(x)	Find the Derivative - d/dx natural log of sin(x)
d()/d(x)2x*y	2y+2xd(y)/d(x)	Find the Derivative - d/dx 2xy
d(x^3)/d(x)	3*x^2	Find the Derivative - d/dx y=x^3
(lim_x→1)(ƒ(x))	ƒ(1)	Evaluate the Limit limit as x approaches 1 of f(x)
d()/d(x)8/(x^2)	−16/(x^3)	Find the Derivative - d/dx 8/(x^2)
(∫_^)(cos(5x)d(x))	1/5sin(5x)+C	Evaluate the Integral integral of cos(5x) with respect to x
(d(x^2)*e^x)/d(x)	x^2e^x+2x*e^x	Find the Derivative - d/dx x^2e^x
(d(−)*x^2)/d(x)	−2*x	Find the Derivative - d/dx -x^2
d(ln(cos(x)))/d(x)	−tan(x)	Find the Derivative - d/dx natural log of cos(x)
d(cos(x))/d(x)	−sin(x)	Find the Derivative - d/dx f(x)=cos(x)
(d(4)*e^x)/d(x)	4*e^x	Find the Derivative - d/dx 4e^x
(∫_^)(x^2e^(x^3)d(x))	1/3*e^(x^3)+C	Evaluate the Integral integral of x^2e^(x^3) with respect to x
(∫_^)(xe^(−x)d(x))	−e^(−x)*(x+1)+C	Evaluate the Integral integral of xe^(-x) with respect to x
d()/d(x)(2x^2+x−1)	4*x+1	Find the Derivative - d/dx 2x^2+x-1
d()/d(x)*x	1	Find the Derivative - d/dx f(x)=x
(d(2)*cos(x))/d(x)	−2*sin(x)	Find the Derivative - d/dx 2cos(x)
d()/d(x)(e^x)/x	(e^x*(x−1))/(x^2)	Find the Derivative - d/dx (e^x)/x
d()/d(x)2ln(x)	2/x	Find the Derivative - d/dx 2 natural log of x
d()/d(x)x^2ln(x)	x(1+2ln(x))	Find the Derivative - d/dx x^2 natural log of x
d()/d(x)1/(x^2+1)	−(2*x)/((x^2+1)^2)	Find the Derivative - d/dx 1/(x^2+1)
(∫_^)(e^x*d(x))	e^x+C	Find the Integral e^x
d()/d(x)x/(x^2+1)	(1−x^2)/((x^2+1)^2)	Find the Derivative - d/dx x/(x^2+1)
d()/d(x)1/(x^2)	−2/(x^3)	Find the Derivative - d/d@VAR f(x)=1/(x^2)
d()/d(x)(∫_^)(x^2d(x))	x^2	Find the Derivative of the Integral integral of x^2 with respect to x
(∫_−2^2)(√(,4−x^2)*d(x))	2*π	Evaluate the Integral
(∫_1^5)(((ln(x))^2)/(x^3)*d(x))	(12−ln(5)−(ln(5))^2)/50	Evaluate the Integral
(∫_^)(1/x*d(x))	ln(x)	Find the Derivative of (1/x) dx
d()/d(x)5/(x^2)	−10/(x^3)	Find the Derivative - d/dx 5/(x^2)
d(x^e)/d(x)	e*x^(e−1)	Find the Derivative - d/dx x^e
(lim_x→0)(sin(3*x)/x)	3	Evaluate the Limit limit as x approaches 0 of (sin(3x))/x
d()/d(x)(x^3+x+4)/(2*x)	(x^3−2)/(x^2)	Find the Derivative - d/dx (x^3+x+4)/(2x)
d()/d(x)*x^2	2*x	Find the Derivative - d/d@VAR f(x)=x^2
d()/d(x)1/(x−1)	−1/((x−1)^2)	Find the Derivative - d/dx 1/(x-1)
d(ln(x^3))/d(x)	3/x	Find the Derivative - d/dx natural log of (x)^3
d(ln(2))/d(x)	0	Find the Derivative - d/dx natural log of 2
cot(0)	undefined	Evaluate cot(0)
(∫_^)(e^(5x)d(x))	(e^(5*x))/5+C	Evaluate the Integral integral of e^(5x) with respect to x
(∫_1^7)(((ln(x))^2)/(x^3)*d(x))	(24−ln(7)−(ln(7))^2)/98	Evaluate the Integral
d()/d(x)(x^2−1)/(x^2+x+1)	(x^2+4*x+1)/((x^2+x+1)^2)	Find the Derivative - d/dx (x^2-1)/(x^2+x+1)
d(ln(4*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 4x
d()/d(x)3/x	−3/(x^2)	Find the Derivative - d/dx 3/x
d(e^5)/d(x)	0	Find the Derivative - d/dx e^5
(∫_1^2)(((ln(x))^2)/(x^3)*d(x))	(3−2ln(2)−2(ln(2))^2)/16	Evaluate the Integral
(∫_^)(sec^3(x)*d(x))	1/2(sec(x)tan(x)+ln(abs(sec(x)+tan(x))))+C	Evaluate the Integral of sec^3(x)dx
(∫_^)((x^2+2x)cos(x)*d(x))	(x^2+2x−2)sin(x)+(2x+2)cos(x)+C	Evaluate the Integral
(∫_1^3)(((ln(x))^2)/(x^3)*d(x))	(4−ln(3)−(ln(3))^2)/18	Evaluate the Integral
(∫_^)(sin(3x)d(x))	−1/3cos(3x)+C	Evaluate the Integral integral of sin(3x) with respect to x
(∫_^)(1/(9x^2+16)d(x))	1/12arctan((3x)/4)+C	Evaluate the Integral
√(,∞)	∞	Evaluate square root of infinity
d(e^x)/d(x)	e^x	Find the Derivative - d/dx y=e^x
d()/d(x)−1/(x^2)	2/(x^3)	Find the Derivative - d/dx -1/(x^2)
d()/d(x)*(x^2−1)	2*x	Find the Derivative - d/dx x^2-1
d(csc(x))/d(x)	−2csc(x)cot(x)	Find the Derivative - d/dx csc(x)^2
(lim_x→8)(cos(x))	cos(8)	Evaluate the Limit limit as x approaches 8 of cos(x)
(∫_^)(e^(4x)d(x))	(e^(4*x))/4+C	Evaluate the Integral integral of e^(4x) with respect to x
(∫_^)(−e^(−x)*d(x))	e^(−x)+C	Evaluate the Integral integral of -e^(-x) with respect to x
(∫_^)(3xd(x))	(3*x^2)/2+C	Evaluate the Integral integral of 3x with respect to x
(∫_1^2)((e^1/(x^4))/(x^5)*d(x))	(e−√(16,e))/4	Evaluate the Integral
d(sin(4*x))/d(x)	4cos(4x)	Find the Derivative - d/dx sin(4x)
(d(6)*e^x)/d(x)	6*e^x	Find the Derivative - d/dx 6e^x
d(sin(5*x))/d(x)	5cos(5x)	Find the Derivative - d/dx sin(5x)
d()/d(x)9/(x^2)	−18/(x^3)	Find the Derivative - d/dx 9/(x^2)
(lim_x→0)(sin(x)/x)	1	Evaluate the Limit ( limit as x approaches 0 of sin(x))/x
(∫_^)(1/x*d(x))	ln(x)	Evaluate the Integral of (1/x) dx
d(√(,x*sin(x)))/d(x)	(sin(x)+xcos(x))/(2√(,xsin(x)))	Find the Derivative - d/dx square root of xsin(x)
d(e^3)/d(x)	0	Find the Derivative - d/dx e^3
x^2+y^2=25	−x/y	Find dy/dx x^2+y^2=25
2xy−y^2=1	y/(y−x)	Find dy/dx 2xy-y^2=1
d()/d(x)5x^2e^(3x)	5xe^(3x)(3*x+2)	Find the Derivative - d/dx y=5x^2e^(3x)
d(e^x)/d(x)	e^x	Find the Derivative - d/dx f(x)=e^x
(d(6)*x^2)/d(x)	12*x	Find the Derivative - d/dx 6x^2
(∫_^)((e^√(,y))/√(,y)*d(y))	2*e^√(,y)+C	Evaluate the Integral
(∫_1^2)((e^1/(x^5))/(x^6)*d(x))	(e−√(32,e))/5	Evaluate the Integral
(∫_^)(xcos(5x)*d(x))	(xsin(5x))/5+cos(5*x)/25+C	Evaluate the Integral integral of xcos(5x) with respect to x
d(e^(1/x))/d(x)	−(e^(1/x))/(x^2)	Find the Derivative - d/dx e^(1/x)
d()/d(x)*(1−cos(x))	sin(x)	Find the Derivative - d/dx 1-cos(x)
d()/d(x)*3√(,x+5)	3/(2√(,x+5))	Find the Derivative - d/dx 3 square root of x+5
d(cos(x))/d(x)	−4cos(x)sin(x)	Find the Derivative - d/dx cos(x)^4
(d(4)*x^3)/d(x)	12*x^2	Find the Derivative - d/dx 4x^3
(∫_^)(sin^3(x)*d(x))	1/3*cos^3(x)−cos(x)+C	Evaluate the Integral integral of sin(x)^3 with respect to x
d()/d(x)9e^x	9*e^x	Find the Derivative - d/dx 9e^x
(d(3)*cos(x))/d(x)	−3*sin(x)	Find the Derivative - d/dx 3cos(x)
d()/d(x)1/(x^4)	−4/(x^5)	Find the Derivative - d/dx 1/(x^4)
2*x+y^2=8,x=y	18	Find the Area Between the Curves 2x+y^2=8 , x=y
(∫_^)(2*d(x))	2*x+C	Evaluate the Integral integral of 2 with respect to x
y=ln(x^2)	ln(x^2)	Graph natural log of x^2
d(8^x)/d(x)	8^x*ln(8)	Find the Derivative - d/dx 8^x
d(x^6)/d(x)	6*x^5	Find the Derivative - d/dx x^6
d()/d(x)7/(x^2)	−14/(x^3)	Find the Derivative - d/dx 7/(x^2)
d(x^(1/3))/d(x)	1/3*x^(−2/3)	Find the Derivative - d/dx x^(1/3)
d(tan(x))/d(x)	sec^2(x)	Find the Derivative - d/dx f(x)=tan(x)
d()/d(x)*(x^2+x)	2*x+1	Find the Derivative - d/dx x^2+x
(d(7)*e^x)/d(x)	7*e^x	Find the Derivative - d/dx 7e^x
(∫_^)(e^(6x)d(x))	(e^(6*x))/6+C	Evaluate the Integral integral of e^(6x) with respect to x
d(tan(2*x))/d(x)	2sec^2(2x)	Find the Derivative - d/dx tan(2x)
d(arccos(x))/d(x)	−1/√(,1−x^2)	Find the Derivative - d/dx arccos(x)
d(cos(5*x))/d(x)	−5sin(5x)	Find the Derivative - d/dx cos(5x)
d()/d(x)√(,x*(x−3))/3	(2x−3)/(6√(,x^2−3x))	Find the Derivative - d/dx ( square root of x(x-3))/3
d()/d(x)sin(x)/x	(x*cos(x)−sin(x))/(x^2)	Find the Derivative - d/dx (sin(x))/x
d()/d(x)(x^2)/8	x/4	Find the Derivative - d/dx (x^2)/8
d()/d(x)6/(x^2)	−12/(x^3)	Find the Derivative - d/dx 6/(x^2)
d()/d(x)*(x^2−5)	2*x	Find the Derivative - d/dx x^2-5
d()/d(x)1/(x^2)	−2/(x^3)	Find the Derivative - d/dx y=1/(x^2)
d()/d(x)*x^(2/3)	2/3*x^(−1/3)	Find the Derivative - d/dx x^(2/3)
d()/d(x)3x^2	6*x	Find the Derivative - d/d@VAR f(x)=3x^2
(∫_^)(cos(3x)d(x))	1/3sin(3x)+C	Evaluate the Integral integral of cos(3x) with respect to x
(lim_x→9)((√(,x)−3)/(x−9))	1/6	Evaluate the Limit
(lim_x→−4)((√(,x^2+9)−5)/(x+4))	−4/5	Evaluate the Limit
csc(0)	undefined	Evaluate csc(0)
(∫_^)(e^(x^3)*d(x))	(∑_n=0^∞)((x^(3n+1))/(n!(3n+1)))+C	Evaluate the Integral integral of e^(x^3) with respect to x
(∫_^)(1/(x^2+1)*d(x))	arctan(x)+C	Evaluate the Integral integral of 1/(x^2+1) with respect to x
(∫_^)(e^(−4x)d(x))	−1/4e^(−4x)+C	Evaluate the Integral integral of e^(-4x) with respect to x
(∫_0^2π)(sin(x)d(x))	0	Evaluate the Integral
(∫_^)(2^x*d(x))	2^x/ln(2)+C	Evaluate the Integral integral of 2^x with respect to x
(∫_^)(1/(1+x^2)*d(x))	arctan(x)+C	Evaluate the Integral integral of 1/(1+x^2) with respect to x
(lim_x→1)((x^2−1)/(x−1))	2	Evaluate the Limit
d()/d(x)1/3*(x^2+2)^(3/2)	x√(,x^2+2)	Find the Derivative - d/dx 1/3(x^2+2)^(3/2)
(d(e^x)*cos(x))/d(x)	e^x*(cos(x)−sin(x))	Find the Derivative - d/dx e^xcos(x)
d(e^(x^3))/d(x)	3x^2e^(x^3)	Find the Derivative - d/dx e^(x^3)
d()/d(x)4/√(,x)	−2/(x√(,x))	Find the Derivative - d/dx 4/( square root of x)
d()/d(x)2/(x^4)	−8/(x^5)	Find the Derivative - d/dx 2/(x^4)
(∫_^)(sec^2(x)*d(x))	tan(x)+C	Find the Integral sec(x)^2
(∫_^)(1/(x^2)*d(x))	−1/x+C	Find the Integral 1/(x^2)
(d(3)*x^3)/d(x)	9*x^2	Find the Derivative - d/dx 3x^3
d(√(,x^2+9))/d(x)	x/√(,x^2+9)	Find the Derivative - d/dx square root of x^2+9
d()/d(x)−1/x	1/(x^2)	Find the Derivative - d/dx -1/x
d()/d(x)*(4−x^2)	−2*x	Find the Derivative - d/dx 4-x^2
d(e^4)/d(x)	0	Find the Derivative - d/dx e^4
d(x^3)/d(x)	3*x^2	Find the Derivative - d/dx f(x)=x^3
(∫_^)(e^√(,x)*d(x))	2e^√(,x)(√(,x)−1)+C	Evaluate the Integral
(∫_^)(5xd(x))	(5*x^2)/2+C	Evaluate the Integral integral of 5x with respect to x
d()/d(x)5/(x^2+5)	(−10*x)/((x^2+5)^2)	Find the Derivative - d/dx 5/(x^2+5)
(∫_^)(cos^2(θ)*d(θ))	θ/2+sin(2*θ)/4+C	Evaluate the Integral
(∫_^)(3*d(x))	3*x+C	Evaluate the Integral integral of 3 with respect to x
(∫_^)(√(3,x)*d(x))	(3*x^4/3)/4+C	Evaluate the Integral
d()/d(x)1/(2*x^2)	−1/(x^3)	Find the Derivative - d/dx 1/2x^2
(d(3)*sin(x))/d(x)	3*cos(x)	Find the Derivative - d/dx 3sin(x)
d()/d(x)5x*ln(x)	5+5*ln(x)	Find the Derivative - d/dx 5x natural log of x
d()/d(x)1/(x^8)	−8/(x^9)	Find the Derivative - d/dx 1/(x^8)
(∫_0^π)(sin(x)*d(x))	2	Evaluate the Integral
(∫_^)(x^2*d(x))	(x^3)/3+C	Find the Integral x^2
d()/d(x)4/(x^2)	−8/(x^3)	Find the Derivative - d/dx 4/(x^2)
d()/d(x)1/(x^7)	−7/(x^8)	Find the Derivative - d/dx 1/(x^7)
d(√(4,x))/d(x)	1/(4√(4,x^3))	Find the Derivative - d/dx fourth root of x
d()/d(x)2/(x^2)	−4/(x^3)	Find the Derivative - d/dx 2/(x^2)
d()/d(x)1/(2*x)	−1/(2*x^2)	Find the Derivative - d/dx 1/(2x)
(lim_x→0)(sec(x))	1	Evaluate the Limit limit as x approaches 0 of sec(x)
(lim_x→0)(tan(x)/x)	1	Evaluate the Limit limit as x approaches 0 of (tan(x))/x
d(x^4)/d(x)	4*x^3	Find the Derivative - d/d@VAR f(x)=x^4
(∫_^)(x^2*d(x))	(x^3)/3+C	Find the Antiderivative x^2
(∫_^)(x√(,1−x^2)*d(x))	−1/3*(1−x^2)^(3/2)+C	Evaluate the Integral
(∫_^)(xe^(3x)*d(x))	1/3xe^(3x)−1/9e^(3*x)+C	Evaluate the Integral integral of xe^(3x) with respect to x
(∫_^)(x^4ln(x)d(x))	(x^5*ln(x))/5−(x^5)/25+C	Evaluate the Integral
d(x^7)/d(x)	7*x^6	Find the Derivative - d/dx x^7
d(√(,x*(x−10)))/d(x)	(x−5)/√(,x^2−10*x)	Find the Derivative - d/dx square root of x(x-10)
(∫_^)(sin(t)√(,1+cos(t))*d(t))	−2/3*(1+cos(t))^(3/2)+C	Evaluate the Integral
(∫_^)(√(,1−x^2)*d(x))	1/2arcsin(x)+1/2x√(,1−x^2)+C	Evaluate the Integral
(lim_x→1)((√(,x)−1)/(x−1))	1/2	Evaluate the Limit
(lim_x→3)((x^2−9)/(x−3))	6	Evaluate the Limit limit as x approaches 3 of (x^2-9)/(x-3)
(∫_^)(e^x*d(x))	e^x+C	Find the Antiderivative e^x
ƒ(x)=x^3−12*x	see full solution →	Find the Local Maxima and Minima f(x)=x^3-12x
y=ln(3*x)	ln(3*x)	Graph natural log of 3x
(lim_x→3)((√(,x+1)−2)/(x−3))	1/4	Evaluate the Limit
(lim_x→π/2)(tan(x))	Does Not Exist	Evaluate the Limit limit as x approaches pi/2 of tan(x)
d(√(,2*x−x^2))/d(x)	(1−x)/√(,2*x−x^2)	Find the Derivative - d/dx square root of 2x-x^2
d()/d(x)3ln(x)	3/x	Find the Derivative - d/dx 3 natural log of x
d()/d(x)2/3*(x^2+1)^(3/2)	2*x√(,x^2+1)	Find the Derivative - d/dx 2/3(x^2+1)^(3/2)
d(ln(x))/d(x)	(3*(ln(x))^2)/x	Find the Derivative - d/dx ( natural log of x)^3
(∫_^)(1/(x^3)*d(x))	−1/(2*x^2)+C	Find the Integral 1/(x^3)
d()/d(x)(x^3−3*x^2+4)/(x^2)	1−8/(x^3)	Find the Derivative - d/dx (x^3-3x^2+4)/(x^2)
d(e^(2*x))/d(x)	2e^(2x)	Find the Derivative - d/dx f(x)=e^(2x)
d(7^x)/d(x)	7^x*ln(7)	Find the Derivative - d/dx 7^x
(∫_^)(ln(2x+1)d(x))	(x+1/2)ln(2x+1)−x+C	Evaluate the Integral
d()/d(x)*12	0	Find the Derivative - d/dx y=12
(d(4)*sin(x))/d(x)	4*cos(x)	Find the Derivative - d/dx 4sin(x)
(∫_^)(4xd(x))	2*x^2+C	Evaluate the Integral integral of 4x with respect to x
(∫_^)(((√(,x)+2)^2)/(5√(,x))*d(x))	see full solution →	Evaluate the Integral
d(x−1)/d(x)	2*(x−1)	Find the Derivative - d/dx (x-1)^2
d()/d(x)(2x^2−5*x+3)	4*x−5	Find the Derivative - d/dx 2x^2-5x+3
d()/d(x)1/(x^2)	−2/(x^3)	Find the Derivative - d/dx f(x)=1/(x^2)
d(√(3,x))/d(x)	1/(3√(3,x^2))	Find the Derivative - d/dx f(x) = cube root of x
d()/d(x)3x^2	6*x	Find the Derivative - d/dx f(x)=3x^2
d()/d(x)*(x^3+x^2)	3x^2+2x	Find the Derivative - d/dx x^3+x^2
d(cos(4*x))/d(x)	−4sin(4x)	Find the Derivative - d/dx cos(4x)
d()/d(x)xe^x	e^x*(x+1)	Find the Derivative - d/dx y=xe^x
d()/d(x)x^9e^x	x^8e^x(x+9)	Find the Derivative - d/dx x^9e^x
d(√(,x^2+y^2))/d(x)	x/√(,x^2+y^2)	Find the Derivative - d/dx square root of x^2+y^2
d()/d(x)*(x^2+2)	2*x	Find the Derivative - d/dx x^2+2
d()/d(x)1/x	−1/(x^2)	Find the Derivative - d/dx y=1/x
d()/d(x)2/(3*x^2)	−4/(3*x^3)	Find the Derivative - d/dx 2/(3x^2)
d()/d(x)*(x^2−x)	2*x−1	Find the Derivative - d/dx x^2-x
(lim_x→0)(sin(5*x)/x)	5	Evaluate the Limit limit as x approaches 0 of (sin(5x))/x
ƒ(x)=ln(x)/x	—	Graph ( natural log of x)/x
tan(−1/3)	−tan(1/3)≈−0.346356	Evaluate tan(-1/3)
(∫_^)(0*d(x))	C	Evaluate the Integral integral of 0 with respect to x
(d(5)*x^3)/d(x)	15*x^2	Find the Derivative - d/dx 5x^3
(∫_0^1)((x−4)/(x^2−5x+6)d(x))	ln(3/8)	Evaluate the Integral
(∫_^)(3x^2d(x))	x^3+C	Evaluate the Integral integral of 3x^2 with respect to x
(∫_^)((2x−3)^2d(x))	(4x^3)/3−6x^2+9*x+C	Evaluate the Integral integral of (2x-3)^2 with respect to x
(∫_^)(2xe^x*d(x))	2xe^x−2*e^x+C	Evaluate the Integral integral of 2xe^x with respect to x
d()/d(x)1/(x^6)	−6/(x^7)	Find the Derivative - d/dx 1/(x^6)
d()/d(x)*(sin(x)+cos(x))	cos(x)−sin(x)	Find the Derivative - d/dx sin(x)+cos(x)
(∫_^)(√(,4−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_0^1)((x−8)/(x^2−7x+10)d(x))	ln(5/16)	Evaluate the Integral
(∫_^)(e^xsin(x)d(x))	(e^x*(sin(x)−cos(x)))/2+C	Evaluate the Integral integral of e^xsin(x) with respect to x
(∫_1^2)(xsin(x^2)d(x))	(cos(1)−cos(4))/2	Evaluate the Integral
(∫_^)(xe^(−2x)*d(x))	−1/4e^(−2x)(2x+1)+C	Evaluate the Integral integral of xe^(-2x) with respect to x
(∫_^)(5*d(x))	5*x+C	Evaluate the Integral integral of 5 with respect to x
d^2(sin(x))/(d(x)^2)	−sin(x)	Find the 2nd Derivative sin(x)
(∫_^)(x^3*d(x))	(x^4)/4+C	Find the Antiderivative x^3
d(√(3,x^4))/d(x)	(4√(3,x))/3	Find the Derivative - d/dx cube root of x^4
d()/d(x)*(x+x^(−1))^3	3(x+x^(−1))^2(1−x^(−2))	Find the Derivative - d/dx (x+x^-1)^3
d()/d(x)(x^2)/9	(2*x)/9	Find the Derivative - d/dx (x^2)/9
d()/d(x)4/x	−4/(x^2)	Find the Derivative - d/dx 4/x
d(e^0)/d(x)	0	Find the Derivative - d/dx e^0
(∫_^)(cos^2(x)*d(x))	x/2+sin(2*x)/4+C	Find the Integral cos(x)^2
d()/d(x)*(x^2−9)	2*x	Find the Derivative - d/dx x^2-9
d()/d(x)1/(x^10)	−10/(x^11)	Find the Derivative - d/dx 1/(x^10)
(∫_^)(sec(x)*d(x))	ln(sec(x)+tan(x))	Evaluate the Integral of sec(x)dx
(∫_−10^10)(sin(xe^(x^2))d(x))	0	Evaluate the Integral
(∫_^)(x^2cos(x)d(x))	x^2sin(x)+2xcos(x)−2sin(x)+C	Evaluate the Integral integral of x^2cos(x) with respect to x
y=sin(x*y)	(ycos(xy))/(1−xcos(xy))	Find dy/dx y=sin(xy)
(∫_^)(tan^3(x)*d(x))	tan^2(x)/2 -ln(sec(x))	Evaluate the Integral of tan^3(x)dx
(∫_^)((9−2017x^2⋅16+6√(5,x)+12e^(4x)−5/x)d(x))	9x-(32272x^3)/3+5x^(6/5)+3e^(4x)-5ln(x)	Evaluate the Integral of (9-(2017x^2)16+6(fifth root of x)+12(e^4x)-5/x)dx
(∫_^)(xe^(−x^2)d(x))	−1/2*e^(−x^2)+C	Evaluate the Integral integral of xe^(-x^2) with respect to x
(∫_^)(1/(x^3)*d(x))	−1/(2*x^2)+C	Evaluate the Integral integral of 1/(x^3) with respect to x
(d(x^4)*e^x)/d(x)	x^4e^x+4x^3*e^x	Find the Derivative - d/dx x^4e^x
(∫_^)(1/(2x)d(x))	1/2*ln(x)	Evaluate the Integral of ( 1/2x) dx
(∫_^)((e^(1/x))/(x^2)*d(x))	−e^(1/x)+C	Evaluate the Integral
d()/d(x)2x^2	4*x	Find the Derivative - d/d@VAR f(x)=2x^2
(∫_^)(tan^2(x)*d(x))	tan(x)−x+C	Find the Integral tan(x)^2
d(ln(x+1))/d(x)	1/(x+1)	Find the Derivative - d/dx natural log of x+1
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative - d/dx f(x)=sec(x)
d()/d(x)(x^2+2x)	2*x+2	Find the Derivative - d/dx x^2+2x
d()/d(x)x^3e^x	x^2e^x(x+3)	Find the Derivative - d/dx y=x^3e^x
1/√(3,x^8)	x^(−8/3)	Simplify 1/( cube root of x^8)
d()/d(x)1/(1+x^2)	−(2*x)/((1+x^2)^2)	Find the Derivative - d/dx 1/(1+x^2)
d()/d(x)x^6e^x	x^5e^x(x+6)	Find the Derivative - d/dx x^6e^x
d()/d(x)(x^2)/5	(2*x)/5	Find the Derivative - d/dx (x^2)/5
d()/d(x)*(x^2−4)	2*x	Find the Derivative - d/dx x^2-4
d()/d(x)2/(x^3)	−6/(x^4)	Find the Derivative - d/dx 2/(x^3)
(d(−)*e^x)/d(x)	−e^x	Find the Derivative - d/dx -e^x
d()/d(x)(4x−x^2)	4 - 2x	Find the Derivative - d/dx 4x-x^2
d()/d(x)*(6/x−2/(x^3)+1/(x^4))	−6/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 6/x-2/(x^3)+1/(x^4)
d()/d(x)(3x^2−x)	6*x−1	Find the Derivative - d/dx 3x^2-x
e^(−8)	1/(e^8)	Simplify e^-8
y=ln(ln(x))	ln(ln(x))* for *x>1	Graph natural log of natural log of x
(lim_x→0)(cos(x))	1	Evaluate the Limit limit as x approaches 0 of cos(x)
(lim_x→4)((√(,x)−2)/(x−4))	1/4	Evaluate the Limit
d()/d(x)(x^2)/7	(2*x)/7	Find the Derivative - d/dx (x^2)/7
(∫_0^27)(√(,3x)d(x))	162	Evaluate the Integral
(∫_^)(x√(,x)*d(x))	2/5*x^(5/2)+C	Evaluate the Integral
(∫_^)(cos(x)*d(x))	sin(x)−sin(x)/3+C	Evaluate the Integral integral of cos(x)^3 with respect to x
(∫_^)(x^(1/2)*d(x))	(2*x^(3/2))/3+C	Evaluate the Integral integral of x^(1/2) with respect to x
(∫_^)(x/(x^2+1)*d(x))	1/2*ln(x^2+1)+C	Evaluate the Integral integral of x/(x^2+1) with respect to x
(∫_^)(arctan(x)*d(x))	xarctan(x)−1/2ln(1+x^2)+C	Evaluate the Integral integral of arctan(x) with respect to x
(∫_^)(2x^2d(x))	(2*x^3)/3+C	Evaluate the Integral integral of 2x^2 with respect to x
(∫_0^π/2)(cos(x)*d(x))	1	Evaluate the Integral
(∫_^)(x^2sin(x)d(x))	−x^2cos(x)+2xsin(x)+2cos(x)+C	Evaluate the Integral integral of x^2sin(x) with respect to x
(∫_^)(sin^2(θ)*d(θ))	θ/2−sin(2*θ)/4+C	Evaluate the Integral
(∫_4^9)(ln(y)/√(,y)*d(y))	12ln(3)−8ln(2)−4	Evaluate the Integral
(∫_^)((9x+4)^2d(x))	27x^3+36x^2+16*x+C	Evaluate the Integral integral of (9x+4)^2 with respect to x
d(x^ln(x))/d(x)	2x^(ln(x)−1)ln(x)	Find the Derivative - d/dx x^( natural log of x)
d()/d(x)1/2*x^2√(,16−x^2)	(32x−3x^3)/(2√(,16−x^2))	Find the Derivative - d/dx 1/2x^2 square root of 16-x^2
y=x,y=3√(,x)	27/2	Find the Area Between the Curves y=x , y=3 square root of x
ƒ(x)=3x^2−12x−8	Local Minimum: *(2,−20), Local Maximum: None	Find the Local Maxima and Minima f(x)=3x^2-12x-8
sin(arctan(x))	x/√(,x^2+1)	Simplify sin(arctan(x))
d()/d(x)−(x^2)/(y^2)	(2x^2d(y)/d(x)−2x*y)/(y^3)	Find the Derivative - d/dx -(x^2)/(y^2)
d(cot^2(x))/d(x)	−2cot(x)csc^2(x)	Find the Derivative - d/dx cot(x)^2
d()/d(x)*(x^2+3)	2*x	Find the Derivative - d/dx x^2+3
(d(p)e^(rt))/d(r)	pte^(r*t)	Find the Derivative - d/dr pe^(rt)
d()/d(x)(x^2−2x)	2*x−2	Find the Derivative - d/dx x^2-2x
d(sin(x))/d(x)	cos(x)	Find the Derivative - d/dx y=sin(x)
d(x^9)/d(x)	9*x^8	Find the Derivative - d/dx x^9
d()/d(x)xcos(x)	cos(x)−x*sin(x)	Find the Derivative - d/dx y=xcos(x)
(∫_^)(sin(2x)d(x))	−cos(2*x)/2+C	Find the Integral sin(2x)
x^3+3x^2y+y^3=8	−(x^2+2xy)/(x^2+y^2)	Find dy/dx x^3+3x^2y+y^3=8
d(√(,9−x^2))/d(x)	−x/√(,9−x^2)	Find the Derivative - d/dx square root of 9-x^2
x^3+y^3=1	−(x^2)/(y^2)	Find dy/dx x^3+y^3=1
d(√(,x^2−1))/d(x)	x/√(,x^2−1)	Find the Derivative - d/dx square root of x^2-1
d()/d(x)x^2e^(−x)	2xe^(−x)−x^2*e^(−x)	Find the Derivative - d/dx x^2e^(-x)
d(e^7)/d(x)	0	Find the Derivative - d/dx e^7
(∑_k=1^5)(k^2)	(∑_k=1^5)(k^2)=55	Evaluate the Summation sum from k=1 to 5 of k^2
d^2()/(d(x)^2)*cos(x^2)	−4x^2cos(x^2)−2*sin(x^2)	Find the 2nd Derivative y=cos(X^2)
(∫_^)(x/√(,1−x^2)*d(x))	−√(,1−x^2)+C	Evaluate the Integral
(∫_^)(xsin(3x)*d(x))	−x/3cos(3x)+1/9sin(3x)+C	Evaluate the Integral integral of xsin(3x) with respect to x
(∫_0^1)((x−6)/(x^2−6x+8)d(x))	−ln(3)	Evaluate the Integral
(∫_^)(xe^(4x)*d(x))	1/4xe^(4x)−1/16e^(4*x)+C	Evaluate the Integral integral of xe^(4x) with respect to x
(∫_^)(xe^(−4x)*d(x))	−1/4xe^(−4x)−1/16e^(−4*x)+C	Evaluate the Integral integral of xe^(-4x) with respect to x
(∫_^)(5^x*d(x))	5^x/ln(5)+C	Evaluate the Integral integral of 5^x with respect to x
(∫_^)(sin(√(,x))/√(,x)*d(x))	−2*cos(√(,x))+C	Evaluate the Integral
(∫_^)(sin(5x)d(x))	−1/5cos(5x)+C	Evaluate the Integral integral of sin(5x) with respect to x
(∫_^)(1/(cos(x)−1)*d(x))	cot(x/2)+C	Evaluate the Integral
(∫_^)(x^5*d(x))	(x^6)/6+C	Evaluate the Integral integral of x^5 with respect to x
(∫_^)(x^4*d(x))	(x^5)/5+C	Evaluate the Integral integral of x^4 with respect to x
(∫_^)(x^3ln(x)d(x))	(x^4*ln(x))/4−(x^4)/16+C	Evaluate the Integral
(∫_^)(7x^2ln(x)*d(x))	(7x^3ln(x))/3−(7*x^3)/9+C	Evaluate the Integral
(∫_^)(ln(x)/(x^2)*d(x))	−(ln(x)+1)/x+C	Evaluate the Integral
d()/d(x)(∫_^)(sin(x)d(x))	sin(x)	Find the Derivative of the Integral integral of sin(x) with respect to x
d(csc(x))/d(x)	−csc(x)*cot(x)	Find the Derivative - d/dx csc(x)
d(e^(5*x))/d(x)	5e^(5x)	Find the Derivative - d/d@VAR f(x)=e^(5x)
d(x^5)/d(x)	5*x^4	Find the Derivative - d/d@VAR f(x)=x^5
d(√(,4−x^2))/d(x)	−x/√(,4−x^2)	Find the Derivative - d/dx square root of 4-x^2
d()/d(x)*(x^2−16/x)	2*x+16/(x^2)	Find the Derivative - d/dx x^2-16/x
d()/d(x)1/√(,x)	−1/(2*x√(,x))	Find the Derivative - d/dx f(x)=1/( square root of x)
d(x^4)/d(x)	4*x^3	Find the Derivative - d/dx f(x)=x^4
d()/d(x)*(x^2+4)	2*x	Find the Derivative - d/dx x^2+4
d(sin(x*y))/d(x)	cos(xy)(xd(y)/d(x)+y)	Find the Derivative - d/dx sin(xy)
d(√(,x^2+4))/d(x)	x/√(,x^2+4)	Find the Derivative - d/dx square root of x^2+4
d(2*x+1)/d(x)	8*x+4	Find the Derivative - d/dx (2x+1)^2
d(ln(3))/d(x)	0	Find the Derivative - d/dx natural log of 3
d(√(,x))/d(x)	1/(2√(,x))	Find the Derivative Using Chain Rule - d/dx square root of x
d(e^y)/d(y)	e^y	Find the Derivative - d/dy e^y
d()/d(y)2x*y	2*x	Find the Derivative - d/dy 2xy
d()/d(x)xy^2	2xyd(y)/d(x)+y^2	Find the Derivative - d/dx xy^2
d()/d(x)(x^3−12x)	3*x^2−12	Find the Derivative - d/dx x^3-12x
(d(3)*x^4)/d(x)	12*x^3	Find the Derivative - d/dx 3x^4
d()/d(x)x/(x^2−1)	−(x^2+1)/((x^2−1)^2)	Find the Derivative - d/dx x/(x^2-1)
d(e^cos(x))/d(x)	−sin(x)*e^cos(x)	Find the Derivative - d/dx e^(cos(x))
d()/d(x)1/ln(x)	−1/(x*ln^2(x))	Find the Derivative - d/dx 1/( natural log of x)
d()/d(x)(x^2)/(x+1)	(x^2+2*x)/((x+1)^2)	Find the Derivative - d/dx (x^2)/(x+1)
d(ln(7*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 7x
e^(1−20x+5x^2)	see full solution →	Find the Local Maxima and Minima e^(1-20x+5x^2)
(lim_x→2)(ƒ(x))	ƒ(2)	Evaluate the Limit limit as x approaches 2 of f(x)
(lim_x→0)(1+x)	e	Evaluate the Limit limit as x approaches 0 of (1+x)^(1/x)
(lim_x→2)((x^2−4)/(x−2))	4	Evaluate the Limit
ƒ(x)=x^3−3*x^2−1,[−3,4]	4, Absolute Min: −55* at *x=−3	Find the Absolute Max and Min over the Interval f(x)=x^3-3x^2-1 , [-3,4]
d(6^x)/d(x)	6^x*ln(6)	Find the Derivative - d/dx 6^x
(∫_−2^1)(√(,3^2−x^2)*d(x))	see full solution →	Evaluate the Integral
d()/d(x)*1	0	Find the Derivative - d/dx 1
(∫_^)(1/(5−3x)d(x))	-1/3ln(5-3x)	Evaluate the Integral of 1/(5-3x)dx
(∫_^)(x^(−3)*d(x))	−1/(2*x^2)+C	Evaluate the Integral integral of x^-3 with respect to x
(∫_^)(4/(x^2+9)*d(x))	4/3*arctan(x/3)+C	Evaluate the Integral integral of 4/(x^2+9) with respect to x
(∫_^)(cos(4x)d(x))	1/4sin(4x)+C	Evaluate the Integral integral of cos(4x) with respect to x
(∫_0^2)(3x^2d(x))	8	Evaluate the Integral
(∫_^)(x^3e^xd(x))	e^x(x^3−3x^2+6*x−6)+C	Evaluate the Integral integral of x^3e^x with respect to x
(∫_^)(x^2e^(−x)d(x))	−e^(−x)(x^2+2x+2)+C	Evaluate the Integral integral of x^2e^(-x) with respect to x
(∫_^)(((ln(x))^2)/x*d(x))	((ln(x))^3)/3+C	Evaluate the Integral
(∫_^)(sin(x)*d(x))	−cos(x)+(2*cos(x))/3−cos(x)/5+C	Evaluate the Integral integral of sin(x)^5 with respect to x
(∫_^)(8x^2ln(x)*d(x))	(8x^3ln(x))/3−(8*x^3)/9+C	Evaluate the Integral
(∫_^)(x^3e^(x^2)d(x))	1/2e^(x^2)(x^2−1)+C	Evaluate the Integral integral of x^3e^(x^2) with respect to x
(∫_5^6)(x√(,x−5)*d(x))	56/15	Evaluate the Integral
d()/d(x)*(3−x^2)	−2*x	Find the Derivative - d/dx 3-x^2
d(ln(1))/d(x)	0	Find the Derivative - d/dx natural log of 1
d()/d(x)7e^x√(,x)	(7e^x(1+2*x))/(2√(,x))	Find the Derivative - d/dx 7e^x square root of x
d(tan^3(x))/d(x)	3tan^2(x)sec^2(x)	Find the Derivative - d/dx tan(x)^3
(lim_x→4)((x^2−16)/(x−4))	8	Evaluate the Limit
(lim_x→8)((√(,x)+√(3,8x)+4)/(√(,4x)+√(3,x)+4))	8−5√(,2)	Evaluate the Limit
(lim_x→2)(x^2)	4	Evaluate the Limit limit as x approaches 2 of x^2
ƒ(x)=x*e^(−x)	see full solution →	Find the Local Maxima and Minima f(x)=xe^(-x)
d()/d(x)*(1−x^2)	−2*x	Find the Derivative - d/d@VAR f(x)=1-x^2
d()/d(x)(xln(x))	1+ln(x)	Find the Derivative - d/d@VAR f(x)=x natural log of x
d()/d(x)*1	0	Find the Derivative - d/d@VAR f(x)=1
(∫_^)(2xd(x))	x^2+C	Find the Antiderivative 2x
(lim_x→8)(ln(x))	ln(8)	Evaluate the Limit
d()/d(x)x/(x−1)	−1/((x−1)^2)	Find the Derivative - d/dx x/(x-1)
d()/d(x)(x^2)/(x^2+3)	(6*x)/((x^2+3)^2)	Find the Derivative - d/dx (x^2)/(x^2+3)
d()/d(x)*(x^2+5)	2*x	Find the Derivative - d/dx x^2+5
d()/d(x)2x*cos(x^2)	2cos(x^2)−4x^2*sin(x^2)	Find the Derivative - d/dx 2xcos(x^2)
d()/d(x)x^3cos(x)	3x^2cos(x)−x^3*sin(x)	Find the Derivative - d/dx x^3cos(x)
d()/d(x)√(,x−4)/√(,x+4)	4/(√(,x−4)*(x+4)^(3/2))	Find the Derivative - d/dx
d()/d(x)(x^2−4)/x	(x^2+4)/(x^2)	Find the Derivative - d/dx y=(x^2-4)/x
d()/d(y)((y^4)/4+1/(8y^2))	y^3−1/(4*y^3)	Find the Derivative - d/dy (y^4)/4+1/(8y^2)
d()/d(x)*(x^3+1)	3*x^2	Find the Derivative - d/dx x^3+1
(∫_^)(csc^2(x)*d(x))	−cot(x)+C	Find the Integral csc(x)^2
d()/d(x)5/x	−5/(x^2)	Find the Derivative - d/dx 5/x
d()/d(x)*2^4⋅0	0	Find the Derivative - d/dx 2^4*0
(∫_^)(x^2e^(2x)*d(x))	(e^(2x))/4(2x^2−2x+1)+C	Evaluate the Integral integral of x^2e^(2x) with respect to x
d(x^(3/2))/d(x)	3/2*x^(1/2)	Find the Derivative - d/dx x^(3/2)
d(ln(sec(x)))/d(x)	tan(x)	Find the Derivative - d/dx natural log of sec(x)
d()/d(x)1/27(9x^2+6)^(3/2)	x√(,9*x^2+6)	Find the Derivative - d/dx 1/27(9x^2+6)^(3/2)
d()/d(x)*5	0	Find the Derivative - d/dx f(x)=5
d()/d(x)(x^2−4x)	2*x−4	Find the Derivative - d/dx x^2-4x
d(e^(−x))/d(x)	−e^(−x)	Find the Derivative - d/dx f(x)=e^(-x)
d(e^x)/d(x)	e^x	Find the Derivative - d/d@VAR f(x)=e^x
d()/d(x)(−(10x)/((x^2+5)^2))	(30*x^2−50)/((x^2+5)^3)	Find the Derivative - d/dx -(10x)/((x^2+5)^2)
d()/d(x)x(x−4)^3	4(x−1)(x−4)^2	Find the Derivative - d/dx y=x(x-4)^3
d(√(,sin(x)))/d(x)	cos(x)/(2√(,sin(x)))	Find the Derivative - d/dx square root of sin(x)
ƒ(x)=csc(x)	csc(x)*(csc^2(x)+cot^2(x))	Find the 2nd Derivative f(x)=csc(x)
(∫_^)(p^5ln(p)d(p))	(p^6*ln(p))/6−(p^6)/36+C	Evaluate the Integral
(∫_^)(1/(e^x)*d(x))	−1/(e^x)+C	Evaluate the Integral integral of 1/(e^x) with respect to x
(∫_^)((7x^2−5)(3x^3+4)d(x))	(7x^6)/2−(15x^4)/4+(28x^3)/3−20x+C	Evaluate the Integral
(∫_^)(x/((x^2+1)^2)*d(x))	−1/(2*(x^2+1))+C	Evaluate the Integral
(∫_−1^2)(x^3*d(x))	15/4	Evaluate the Integral
(∫_^)(2e^xd(x))	2*e^x+C	Evaluate the Integral integral of 2e^x with respect to x
(∫_^)(1/(xln(x))d(x))	ln(ln(x))	Evaluate the Integral of 1/(xln(x)) dx
(∫_^)(√(,x)ln(x)d(x))	2/3x^(3/2)ln(x)−4/9*x^(3/2)+C	Evaluate the Integral
(∫_0^8)(√(,8x)d(x))	128/3	Evaluate the Integral
(∫_^)(x^3e^(x^4)d(x))	(e^(x^4))/4+C	Evaluate the Integral integral of x^3e^(x^4) with respect to x
arcsin(1)	π/2	Evaluate arcsin(1)
ƒ(x)=x^3−3*x^2−1,[−3,2]	0, Absolute Min: −55* at *x=−3	Find the Absolute Max and Min over the Interval f(x)=x^3-3x^2-1 , [-3,2]
ƒ(x)=0.8x^3−4x^2−1,[−30,4]	see full solution →	Find the Absolute Max and Min over the Interval f(x)=0.8x^3-4x^2-1 , [-30,4]
cos(2)	cos(2)≈−0.4161	Evaluate cos(2)
d()/d(x)*ln(x)	1/x	Find the Derivative - d/dx y = natural log of x
x^2y+y^2x=−2	−(2xy+y^2)/(x^2+2xy)	Find dy/dx x^2y+y^2x=-2
4cos(x)sin(y)=1	tan(x)*tan(y)	Find dy/dx 4cos(x)sin(y)=1
y=16√(4,4*x^4+4)	(64x^3)/((4x^4+4)^(3/4))	Find dy/dx y=16 fourth root of 4x^4+4
d()/d(x)*x^cos(x)	see full solution →	Find the Derivative - d/d@VAR f(x)=x^(cos(x))
(∫_^)(e^(x^2)*d(x))	√(,π)/2*erfi(x)+C	Find the Integral e^(x^2)
d()/d(x)*(9−x^2)	−2*x	Find the Derivative - d/dx 9-x^2
d()/d(x)(4/(x^2)−10x^3)	−8/(x^3)−30*x^2	Find the Derivative - d/dx 4/(x^2)-10x^3
d(sec(x^2))/d(x)	2xsec(x^2)*tan(x^2)	Find the Derivative - d/dx sec(x^2)
d(sin(ln(x)))/d(x)	cos(ln(x))/x	Find the Derivative - d/dx sin( natural log of x)
d()/d(x)(x^2)/4	x/2	Find the Derivative - d/dx (x^2)/4
d(ln(1+x))/d(x)	1/(1+x)	Find the Derivative - d/dx natural log of 1+x
d(√(,25−x^2))/d(x)	−x/√(,25−x^2)	Find the Derivative - d/dx square root of 25-x^2
d()/d(x)x^2(1−2*x)	2x−6x^2	Find the Derivative - d/dx x^2(1-2x)
d()/d(x)(9√(,x))/x	−9/(2*x√(,x))	Find the Derivative - d/dx y=(9 square root of x)/x
d()/d(x)ln(x)/x	(1−ln(x))/(x^2)	Find the Derivative - d/dx y=( natural log of x)/x
(∫_^)(xe^xd(x))	(x−1)*e^x+C	Find the Integral xe^x
(∫_^)(x^3*d(x))	(x^4)/4+C	Find the Integral x^3
d()/d(x)*(−csc(x)−sin(x))	csc(x)*cot(x)−cos(x)	Find the Derivative - d/dx -csc(x)-sin(x)
d(sec(2*x))/d(x)	2sec(2x)tan(2x)	Find the Derivative - d/dx sec(2x)
(∫_^)(xln(x)d(x))	(x^2*ln(x))/2−(x^2)/4+C	Evaluate the Integral
d()/d(x)(2x^2+x−1)	4*x+1	Find the Derivative - d/d@VAR f(X)=2x^2+x-1
(d(−)*csc(x))/d(x)	csc(x)*cot(x)	Find the Derivative - d/dx -csc(x)
(∫_^)(x^2√(,x^3+1)*d(x))	2/9*(x^3+1)^(3/2)+C	Evaluate the Integral
d()/d(x)*(4√(,x)−5/(x^2))	2/√(,x)+10/(x^3)	Find the Derivative - d/dx 4 square root of x-5/(x^2)
(d(5)*sin(x))/d(x)	5*cos(x)	Find the Derivative - d/dx 5sin(x)
d()/d(x)1/(x+1)	−1/((x+1)^2)	Find the Derivative - d/dx 1/(x+1)
d()/d(x)*(1−sin(x))	−cos(x)	Find the Derivative - d/dx 1-sin(x)
d()/d(x)(3x^(2/3)−2*x)	2/(x^(1/3))−2	Find the Derivative - d/dx 3x^(2/3)-2x
d()/d(x)*(x^2−3)	2*x	Find the Derivative - d/dx x^2-3
d()/d(x)√(,x+4)	1/(2√(,x+4))	Find the Derivative - d/dx y = square root of x+4
d()/d(x)x^3ln(x)	x^2(1+3ln(x))	Find the Derivative - d/dx x^3 natural log of x
d()/d(x)1/(x^9)	−9/(x^10)	Find the Derivative - d/dx 1/(x^9)
d()/d(x)x^2y	2xy+x^2d(y)/d(x)	Find the Derivative - d/dx x^2y
d()/d(x)(3x−8)ln(2x^5+3)	(30x^5−80x^4)/(2x^5+3)+3ln(2*x^5+3)	Find the Derivative - d/dx (3x-8) natural log of 2x^5+3
d()/d(x)*(x^3−x)	3*x^2−1	Find the Derivative - d/dx x^3-x
d()/d(x)(x^2)/(x−1)	(x^2−2*x)/((x−1)^2)	Find the Derivative - d/dx (x^2)/(x-1)
d()/d(x)1/(1+x)	−1/((1+x)^2)	Find the Derivative - d/dx 1/(1+x)
d()/d(x)3e^x√(,x)	3e^x√(,x)+(3e^x)/(2√(,x))	Find the Derivative - d/dx 3e^x square root of x
d()/d(x)1/(x−2)	−1/((x−2)^2)	Find the Derivative - d/dx 1/(x-2)
(d(8)*x^2)/d(x)	16*x	Find the Derivative - d/dx 8x^2
d(e^t)/d(t)	e^t	Find the Derivative - d/dt e^t
(lim_x→3)(ƒ(x))	ƒ(3)	Evaluate the Limit limit as x approaches 3 of f(x)
(lim_x→π)(cot(x))	Does Not Exist	Evaluate the Limit limit as x approaches pi of cot(x)
ƒ(x)=x^2*ln(x)	—	Graph x^2 natural log of x
(ln(x))^2	(ln(x))^2	Graph ( natural log of x)^2
y=x,y=x^2	1/6	Find the Area Between the Curves y=x , y=x^2
(lim_x→0)(x^2)	0	Evaluate the Limit limit as x approaches 0 of x^2
(lim_x→−∞)(e^x)	0	Evaluate the Limit
(lim_x→9)((√(,x)−3)/(x−9))	1/6	Evaluate the Limit
(lim_x→π/2)(sin(x))	1	Evaluate the Limit limit as x approaches pi/2 of sin(x)
(lim_h→0)(((x+h)^3−x^3)/h)	3*x^2	Evaluate the Limit
sin((3*π)/2)	−1	Evaluate sin((3pi)/2)
cot(π/4)	1	Evaluate cot(pi/4)
ƒ(x)=x^2−5,[0,3]	Absolute Max: *4, Absolute Min: −5	Find the Absolute Max and Min over the Interval f(x)=x^2-5 , [0,3]
ƒ(x)=x^4−4*x^2,[−3,4]	4, Absolute Min: −4* at *x=±√(,2)	Find the Absolute Max and Min over the Interval f(x)=x^4-4x^2 , [-3,4]
ƒ(x)=6*x^2,[1,3]	54,Absolute Min=6	Find the Absolute Max and Min over the Interval f(x)=6x^2 , [1,3]
(∫_^)(2/x*d(x))	2*ln(x)	Evaluate the Integral of 2/x dx
(∫_1^2)(xln(x)d(x))	2*ln(2)−3/4	Evaluate the Integral
(∫_^)(e^y*d(y))	e^y+C	Evaluate the Integral integral of e^y with respect to y
(∫_^)(ln(3x)d(x))	xln(3x)−x+C	Evaluate the Integral
(∫_^)(1/(y^2)*d(y))	−1/y+C	Evaluate the Integral integral of 1/(y^2) with respect to y
(∫_^)(1/√(,1−x^2)*d(x))	arcsin(x)+C	Evaluate the Integral
(∫_^)(−3*d(x))	−3*x+C	Evaluate the Integral integral of -3 with respect to x
(∫_0^1)((x^2+6)e^(−x)d(x))	8−11/e	Evaluate the Integral
(∫_^)(2td(t))	t^2+C	Evaluate the Integral integral of 2t with respect to t
(∫_2^3)(x√(,x−2)*d(x))	26/15	Evaluate the Integral
(∫_^)((t^2)/√(,1−t^6)*d(t))	1/3*arcsin(t^3)+C	Evaluate the Integral
(∫_4^9)(√(,x)*d(x))	38/3	Evaluate the Integral
(∫_^)(e^xcos(x)d(x))	(e^x*(cos(x)+sin(x)))/2+C	Evaluate the Integral integral of e^xcos(x) with respect to x
d()/d(x)((x+5)*x)/(x+1)	(x^2+2*x+5)/((x+1)^2)	Find the Derivative - d/dx y=((x+5)x)/(x+1)
d()/d(x)(x^2)/6	x/3	Find the Derivative - d/dx (x^2)/6
d()/d(x)(3√(,x))/x	−3/(2*x√(,x))	Find the Derivative - d/dx y=(3 square root of x)/x
(∑_i=1^4)(6^(i−1))	(∑_i=1^4)(6^(i−1))=259	Evaluate the Summation sum from i=1 to 4 of 6^(i-1)
(lim_t→0)(1/t−1/(t^2+t))	1	Evaluate the Limit limit as t approaches 0 of 1/t-1/(t^2+t)
(lim_x→4)((√(,x+5)−3)/(x−4))	1/6	Evaluate the Limit
(lim_x→3)((x^2−9)/(x−3))	6	Evaluate the Limit
(lim_x→2)((x^2+x−6)/(x−2))	5	Evaluate the Limit
(lim_x→0)(sin(2*x)/x)	2	Evaluate the Limit limit as x approaches 0 of (sin(2x))/x
(lim_x→25)((√(,x)−5)/(x−25))	1/10	Evaluate the Limit
(lim_x→1)(1/(x−1))	Does Not Exist	Evaluate the Limit limit as x approaches 1 of 1/(x-1)
y=2*ln(x)	2*ln(x)	Graph 2 natural log of x
(d(−)2x*sin(x^2))/d(x)	−4x^2cos(x^2)−2*sin(x^2)	Find the Derivative - d/dx -2xsin(x^2)
d()/d(x)(x^2+4*x+3)/√(,x)	(3x^2+4x−3)/(2*x√(,x))	Find the Derivative - d/dx (x^2+4x+3)/( square root of x)
d(x^8)/d(x)	8*x^7	Find the Derivative - d/dx x^8
d()/d(x)√(,x+6)	1/(2√(,x+6))	Find the Derivative - d/dx y = square root of x+6
d()/d(x)x/ln(x)	(ln(x)−1)/((ln(x))^2)	Find the Derivative - d/dx x/( natural log of x)
d(x+1)/d(x)	2*(x+1)	Find the Derivative - d/dx (x+1)^2
d(√(4,x^3))/d(x)	3/(4√(4,x))	Find the Derivative - d/dx fourth root of x^3
(d(2)*x^4)/d(x)	8*x^3	Find the Derivative - d/dx 2x^4
d()/d(x)((x+3)*x)/(x+1)	(x^2+2*x+3)/((x+1)^2)	Find the Derivative - d/dx y=((x+3)x)/(x+1)
d()/d(x)d(y)/d(x)	d^2(y)/(d(x)^2)	Find the Derivative - d/dd (dy)/(dx)
d()/d(y)(1/(y^2)−9/(y^4))(y+3*y^3)	3+26/(y^2)+27/(y^4)	Find the Derivative - d/dy (1/(y^2)-9/(y^4))(y+3y^3)
d()/d(x)sec(x)tan(x)	sec^3(x)+sec(x)*tan^2(x)	Find the Derivative - d/dZ y=sec(x)tan(x)
(d(−)*x^3)/d(x)	−3*x^2	Find the Derivative - d/dx -x^3
d(ln(e^x))/d(x)	1	Find the Derivative - d/dx natural log of e^x
d()/d(x)(e^x)/(1+x)	(x*e^x)/((1+x)^2)	Find the Derivative - d/dx (e^x)/(1+x)
d()/d(x)6/x	−6/(x^2)	Find the Derivative - d/dx 6/x
(∫_^)(−cos(x)*d(x))	−sin(x)+C	Find the Integral -cos(x)
d()/d(x)(x^2)/3	(2*x)/3	Find the Derivative - d/dx (x^2)/3
d(csc(x))/d(x)	−csc(x)*cot(x)	Find the Derivative - d/dx f(x)=csc(x)
d(cos(x*y))/d(x)	−xsin(xy)d(y)/d(x)−ysin(xy)	Find the Derivative - d/dx cos(xy)
(d(e^x)*sin(x))/d(x)	e^x*(sin(x)+cos(x))	Find the Derivative - d/dx e^xsin(x)
x^2+y^2=1	−x/y	Find dy/dx x^2+y^2=1
d()/d(x)(2x^2−7*x+5)	4*x−7	Find the Derivative - d/dx 2x^2-7x+5
(d(7)*x^2)/d(x)	14*x	Find the Derivative - d/dx 7x^2
d()/d(x)(3x+2√(,x)+32/(x^2))	3+1/√(,x)−64/(x^3)	Find the Derivative - d/dx 3x+2 square root of x+32/(x^2)
(∫_^)(x^2cos(3x)*d(x))	see full solution →	Evaluate the Integral integral of x^2cos(3x) with respect to x
d^2()/(d(x)^2)√(,x+3)	−1/(4*(x+3)^(3/2))	Find the 2nd Derivative y = square root of x+3
ƒ(x)=sec(x)	sec(x)*(sec^2(x)+tan^2(x))	Find the 2nd Derivative f(x)=sec(x)
(∫_−5^5)(√(,25−x^2)*d(x))	(25*π)/2	Evaluate the Integral
(∫_^)(1/(x(ln(x))^2)d(x))	−1/ln(x)+C	Evaluate the Integral
(∫_^)(e^x√(,1+e^x)*d(x))	2/3*(1+e^x)^(3/2)+C	Evaluate the Integral
(∫_0^1)((x^2+4)e^(−x)d(x))	6−9/e	Evaluate the Integral
(∫_^)(1/t*d(t))	ln(t)	Evaluate the Integral
(∫_^)(z^3e^zd(z))	e^z(z^3−3z^2+6*z−6)+C	Evaluate the Integral integral of z^3e^z with respect to z
(∫_^)(sin(√(,x))*d(x))	−2√(,x)cos(√(,x))+2sin(√(,x))+C	Evaluate the Integral
(∫_0^2)(√(,4−x^2)*d(x))	π	Evaluate the Integral
(∫_0^π)(cos^2(x)*d(x))	π/2	Evaluate the Integral
(∫_25^3)((6ln(y))/√(,y)d(y))	12√(,3)ln(3)−24√(,3)−120ln(5)+120	Evaluate the Integral
(∫_^)((12x+5)^2d(x))	((12*x+5)^3)/36+C	Evaluate the Integral integral of (12x+5)^2 with respect to x
(∫_^)(arctan(4t)d(t))	tarctan(4t)−1/8ln(1+16t^2)+C	Evaluate the Integral integral of arctan(4t) with respect to t
(∫_0^1)((r^3)/√(,16+r^2)*d(r))	(128−31√(,17))/3	Evaluate the Integral
(∫_^)(cos(x)e^sin(x)d(x))	e^sin(x)+C	Evaluate the Integral
2(∫_^)(xd(x))	x^2+C	Evaluate the Integral 2 integral of x with respect to x
(∫_−3^3)(√(,9−x^2)*d(x))	(9*π)/2	Evaluate the Integral
(∫_^)(3/x*d(x))	3*ln(x)	Evaluate the Integral
(∫_0^1)(4x^5−5x^4*d(x))	−1/3	Evaluate the Integral
(lim_x→−24)((√(,x^2+49)−25)/(x+24))	−24/25	Evaluate the Limit
(∫_0^45)(1/√(,t+4)*d(t))	10	Evaluate the Integral
ƒ(x)=5x^2−3x−1,[−1,3]	3, Absolute Min: −1.45* at *x=0.3	Find the Absolute Max and Min over the Interval f(x)=5x^2-3x-1 , [-1,3]
9*x^2+y^2=9	−(9*x)/y	Find dy/dx 9x^2+y^2=9
x^2+y^2=16	−x/y	Find dy/dx x^2+y^2=16
d(sin(x))/d(x)	4sin(x)cos(x)	Find the Derivative - d/dx sin(x)^4
d()/d(x)*(x^2+1)	2*x	Find the Derivative - d/d@VAR f(x)=x^2+1
d()/d(x)*(x^3+x^2)	3x^2+2x	Find the Derivative - d/d@VAR f(x)=x^3+x^2
d(√(5,6*x))/d(x)	6/(5√(5,(6*x)^4))	Find the Derivative - d/dx fifth root of 6x
d()/d(x)3x^2	6*x	Find the Derivative - d/dx y=3x^2
d()/d(x)(4x−x^2)	4 - 2x	Find the Derivative - d/dx y=4x-x^2
d(√(,x^2+3))/d(x)	x/√(,x^2+3)	Find the Derivative - d/dx square root of x^2+3
d()/d(x)8/(3*x^2)	−16/(3*x^3)	Find the Derivative - d/dx y=8/(3x^2)
d(e^sin(x))/d(x)	e^sin(x)*cos(x)	Find the Derivative - d/dx e^(sin(x))
d(e^(x^5))/d(x)	5x^4e^(x^5)	Find the Derivative - d/dx e^(x^5)
d(6*x+1)/d(x)	72*x+12	Find the Derivative - d/dx (6x+1)^2
(d(8)*e^x)/d(x)	8*e^x	Find the Derivative - d/dx 8e^x
d(e^(1−20x+5x^2))/d(x)	(10x−20)e^(1−20x+5x^2)	Find the Derivative - d/dx e^(1-20x+5x^2)
e^∞	∞	Simplify e^infinity
d()/d(t)d(at^2+bt+c)/d(t)	2*a	Find the Derivative - d/dt d/(dt)(at^2+bt+c)
d()/d(x)x(x^2+1)	3*x^2+1	Find the Derivative - d/dx x(x^2+1)
d()/d(x)(2*x)/(x^2+1)	(2*(1−x^2))/((x^2+1)^2)	Find the Derivative - d/dx (2x)/(x^2+1)
d()/d(x)*(x+2/x)	1−2/(x^2)	Find the Derivative - d/dx x+2/x
d()/d(x)x(x^2−5/x)	3*x^2	Find the Derivative - d/dx x(x^2-5/x)
d()/d(x)x/3	1/3	Find the Derivative - d/dx x/3
d(√(,1−6*x))/d(x)	(−3)/√(,1−6*x)	Find the Derivative - d/dx square root of 1-6x
d()/d(x)x(x−4)^3	4(x−1)(x−4)^2	Find the Derivative - d/dx x(x-4)^3
d()/d(x)x/(x+2)	2/((x+2)^2)	Find the Derivative - d/dx x/(x+2)
d()/d(x)x/(x^2+2)	(2−x^2)/((x^2+2)^2)	Find the Derivative - d/dx x/(x^2+2)
d()/d(x)x/(x^2+9)	(9−x^2)/((x^2+9)^2)	Find the Derivative - d/dx x/(x^2+9)
d()/d(x)x^8e^x	x^8e^x+8x^7*e^x	Find the Derivative - d/dx x^8e^x
(d(2)*tan(x))/d(x)	2*sec^2(x)	Find the Derivative - d/dx 2tan(x)
d(e^6)/d(x)	0	Find the Derivative - d/dx e^6
d(tan((π*x)/2))/d(x)	π/2sec^2((πx)/2)	Find the Derivative - d/dx tan((pix)/2)
d(ln(5))/d(x)	0	Find the Derivative - d/dx natural log of 5
d()/d(x)1/(x^5)	−5/(x^6)	Find the Derivative - d/dx y=1/(x^5)
1/8	0.125	Simplify 1/8
(x+8)*(24/x+12)	12*x+120+192/x	Simplify (x+8)(24/x+12)
v=√(,3^2+(−1)^2)	√(,10)	Solve for v v = square root of 3^2+(-1)^2
ln(sin(x))	ln(sin(x))	Graph natural log of sin(x)
(lim_x→0)(tan(x)/x)	1	Evaluate the Limit ( limit as x approaches 0 of tan(x))/x
(lim_x→0)(cos(1/x))	Does Not Exist	Evaluate the Limit limit as x approaches 0 of cos(1/x)
(lim_x→−3)((x^2−9)/(x+3))	−6	Evaluate the Limit
(lim_x→4)((√(,x)−2)/(x−4))	1/4	Evaluate the Limit
(lim_x→∞)(e^x)	∞	Evaluate the Limit limit as x approaches infinity of e^x
(∫_^)(3xd(x))	3/2*x^2+C	Find the Antiderivative 3x
(∫_^)(e^(2x)d(x))	(e^(2*x))/2+C	Find the Antiderivative e^(2x)
(lim_x→3)((x−3)/(x−3))	1	Evaluate the Limit limit as x approaches 3 of (x-3)/(x-3)
(lim_x→2)((x^2−4)/(x−2))	4	Evaluate the Limit limit as x approaches 2 of (x^2-4)/(x-2)
(lim_x→−2)((x+2)/(x^3+8))	1/12	Evaluate the Limit
(lim_x→2)((x^3−8)/(x−2))	12	Evaluate the Limit limit as x approaches 2 of (x^3-8)/(x-2)
d()/d(x)(e^x)/(x^2)	(e^x*(x−2))/(x^3)	Find the Derivative - d/dx (e^x)/(x^2)
e^(−0)	1	Evaluate e^(-0)
ƒ(x)=3*x^2−1,[1,3]	26,Absolute Min=2	Find the Absolute Max and Min over the Interval f(x)=3x^2-1 , [1,3]
ƒ(x)=1/2x^4+2x^3	Inflection Points: *(−2,−8),(0,0)	Find the Inflection Points f(x)=1/2x^4+2x^3
ƒ(x)=5x^2−2x,g(x)=8x+3,ƒ(g(k))	320k^2+224k+39	Solve the Function Operation f(x)=5x^2-2x , g(x)=8x+3 , f(g(k))
(lim_x→1)((x^2−1)/(x−1))	2	Evaluate the Limit limit as x approaches 1 of (x^2-1)/(x-1)
d()/d(x)(∫_^)(2x*d(x))	2*x	Find the Derivative of the Integral integral of 2x with respect to x
(∫_^)(x^2e^(3x)*d(x))	(e^(3x))/27(9x^2−6x+2)+C	Evaluate the Integral integral of x^2e^(3x) with respect to x
(∫_^)(10xd(x))	5*x^2+C	Evaluate the Integral integral of 10x with respect to x
(∫_1^9)(√(,x)*d(x))	52/3	Evaluate the Integral
(∫_0^2)(2x^2d(x))	16/3	Evaluate the Integral
d()/d(x)√(,x−9)/√(,x+9)	9/(√(,x−9)*(x+9)^(3/2))	Find the Derivative - d/dx
(∫_^)(2x^2ln(x)*d(x))	(2x^3ln(x))/3−(2*x^3)/9+C	Evaluate the Integral
(∫_^)(ln(x)*d(x))	x*ln(x)−x+C	Evaluate the Integral integral of log of x with respect to x
(∫_^)(xsin(x^2)d(x))	−1/2*cos(x^2)+C	Evaluate the Integral integral of xsin(x^2) with respect to x
(∫_^)(x√(,x+2)*d(x))	2/5(x+2)^(5/2)−4/3(x+2)^(3/2)+C	Evaluate the Integral
(∫_^)(9x^3d(x))	(9*x^4)/4+C	Evaluate the Integral integral of 9x^3 with respect to x
(∫_^)(9xd(x))	(9*x^2)/2+C	Evaluate the Integral integral of 9x with respect to x
(∫_^)(√(,8x+1)d(x))	1/12(8x+1)^(3/2)+C	Evaluate the Integral
(∫_^)(sin(x^2)*d(x))	see full solution →	Evaluate the Integral integral of sin(x^2) with respect to x
(∫_^)(sec^2(x)tan(x)d(x))	tan^2(x)/2+C	Evaluate the Integral
(∫_^)(xsin(2x)*d(x))	−x/2cos(2x)+1/4sin(2x)+C	Evaluate the Integral integral of xsin(2x) with respect to x
(∫_^)(e^(2x)x^2*d(x))	(e^(2x)(2x^2−2x+1))/4+C	Evaluate the Integral integral of e^(2x)x^2 with respect to x
(∫_^)((ln(t))^2*d(t))	t(ln(t))^2−2tln(t)+2t+C	Evaluate the Integral
ƒ(x)=ln(x)	−1/(x^2)	Find the 2nd Derivative f(x) = natural log of x
tan(x)	2sec^2(x)tan(x)	Find the 2nd Derivative tan(x)
(∫_^)((x+1)^2*d(x))	(x^3)/3+x^2+x+C	Evaluate the Integral integral of (x+1)^2 with respect to x
(∫_^)(sin(4x)d(x))	−1/4cos(4x)+C	Evaluate the Integral integral of sin(4x) with respect to x
d()/d(x)*x^x	x^x*(ln(x)+1)	Find the Derivative - d/dx y=x^x
d(x−2)/d(x)	2*(x−2)	Find the Derivative - d/dx (x-2)^2
d()/d(x)*(x+1/x)	1−1/(x^2)	Find the Derivative - d/dx x+1/x
d^2()/(d(x)^2)1/x	2/(x^3)	Find the 2nd Derivative 1/x
d()/d(x)*(√(,x))^x	(√(,x))^x*((ln(x)+1)/2)	Find the Derivative - d/dx y=( square root of x)^x
d(x^2+1)/d(x)	4x(x^2+1)	Find the Derivative - d/dx (x^2+1)^2
(∫_^)(3x^2d(x))	x^3+C	Find the Antiderivative f(x)=3x^2
(∫_^)(x^(1/2)*d(x))	(2*x^(3/2))/3+C	Find the Antiderivative x^(1/2)
(lim_x→4)((x−4)/(x−4))	1	Evaluate the Limit limit as x approaches 4 of (x-4)/(x-4)
(lim_x→−12)((√(,x^2+25)−13)/(x+12))	−12/13	Evaluate the Limit
(lim_x→−1)(ƒ(x))	ƒ*(−1)	Evaluate the Limit limit as x approaches -1 of f(x)
(lim_x→0)((√(,x+4)−2)/x)	1/4	Evaluate the Limit
ƒ(x)=ln(x)/(x^2)	—	Graph ( natural log of x)/(x^2)
y=ln(x^3)	ln(x^3)=3ln(x) for *x>0	Graph natural log of x^3
d()/d(x)*(√(,x)+5/√(,x))	1/(2√(,x))−5/(2*x√(,x))	Find the Derivative - d/dx square root of x+5/( square root of x)
d()/d(x)(x^4)/4	x^3	Find the Derivative - d/dx (x^4)/4
d()/d(x)5e^x*cos(x)	5e^x(cos(x)−sin(x))	Find the Derivative - d/dx 5e^xcos(x)
d(x^sin(x))/d(x)	x^sin(x)(cos(x)ln(x)+sin(x)/x)	Find the Derivative - d/dx x^(sin(x))
d()/d(x)((x+6)*x)/(x+1)	(x^2+2*x+6)/((x+1)^2)	Find the Derivative - d/dx y=((x+6)x)/(x+1)
d(e^(x^4))/d(x)	4x^3e^(x^4)	Find the Derivative - d/dx e^(x^4)
d(tan(x^4+1))/d(x)	8x^3tan(x^4+1)*sec^2(x^4+1)	Find the Derivative - d/dx tan(x^4+1)^2
d()/d(x)√(,x+12)	1/(2√(,x+12))	Find the Derivative - d/dx y = square root of x+12
d(x^cos(x))/d(x)	see full solution →	Find the Derivative - d/dx x^(cos(x))
d()/d(x)(x^3+2x)	3*x^2+2	Find the Derivative - d/dx x^3+2x
d()/d(x)(2x^2−x)	4*x−1	Find the Derivative - d/dx 2x^2-x
d()/d(x)(−20e^(1−4*x)+20)	80e^(1−4x)	Find the Derivative - d/dx -20e^(1-4x)+20
d()/d(x)((x+7)*x)/(x+1)	(x^2+2*x+7)/((x+1)^2)	Find the Derivative - d/dx y=((x+7)x)/(x+1)
d(tan(x))/d(x)	sec^2(x)	Find the Derivative - d/dx y=tan(x)
d()/d(x)3x*y	3xd(y)/d(x)+3y	Find the Derivative - d/dx 3xy
d(e^(−(5−3*x)^2))/d(x)	(30−18x)e^(−(5−3*x)^2)	Find the Derivative - d/dx e^(-(5-3x)^2)
d()/d(t)−1/((2+t)^2)	2/((2+t)^3)	Find the Derivative - d/dt -1/((2+t)^2)
d()/d(x)√(,x)/(x^3+1)	(1−5x^3)/(2√(,x)(x^3+1)^2)	Find the Derivative - d/dx ( square root of x)/(x^3+1)
d()/d(x)(x^3+x+1)/x	2*x−1/(x^2)	Find the Derivative - d/dx (x^3+x+1)/x
d()/d(x)*(1+cos(x))	−sin(x)	Find the Derivative - d/dx 1+cos(x)
d()/d(x)2e^x*cos(x)	2e^x(cos(x)−sin(x))	Find the Derivative - d/dx 2e^xcos(x)
d()/d(x)ln(5x)	1/x	Find the Derivative - d/dx y = natural log of 5x
d()/d(x)x/(x^2+1)	(1−x^2)/((x^2+1)^2)	Find the Derivative Using Quotient Rule - d/dx x/(x^2+1)
d()/d(x)*(1+cos^2(x))	−sin(2*x)	Find the Derivative - d/dx 1+cos(x)^2
d(ln(x))/d(x)	(4*(ln(x))^3)/x	Find the Derivative - d/dx ( natural log of x)^4
d()/d(x)3/(x^3)	−9/(x^4)	Find the Derivative - d/dx 3/(x^3)
d()/d(x)(x^2+1)(x^2−1)	4*x^3	Find the Derivative - d/dx (x^2+1)(x^2-1)
d()/d(x)*(x^2+x−2)	2*x+1	Find the Derivative - d/dx x^2+x-2
d(sin(x^3))/d(x)	3x^2cos(x^3)	Find the Derivative - d/dx sin(x^3)
d()/d(x)x^3sin(x)	x^3cos(x)+3x^2*sin(x)	Find the Derivative - d/dx x^3sin(x)
(∫_^)(e^(−x)*d(x))	−e^(−x)+C	Find the Antiderivative e^(-x)
(d(x)*e^x)/d(x)	e^x*(x+1)	Find the Derivative - d/dx f(x)=xe^x
d()/d(x)*3√(,x)	3/(2√(,x))	Find the Derivative - d/dx f(x)=3 square root of x
(∫_^)(cos(5x)d(x))	1/5sin(5x)+C	Find the Integral cos(5x)
x^2+y^2=4	−x/y	Find dy/dx x^2+y^2=4
x^2+y^2=9	−x/y	Find dy/dx x^2+y^2=9
tan(x−y)=y/(1+x^2)	see full solution →	Find dy/dx tan(x-y)=y/(1+x^2)
d()/d(x)x(x^2+5)^(1/3)	(5x^2+15)/(3(x^2+5)^(2/3))	Find the Derivative - d/dx x(x^2+5)^(1/3)
d(√(,1+x^2))/d(x)	x/√(,1+x^2)	Find the Derivative - d/dx square root of 1+x^2
d()/d(x)*(2/x−2/(x^3)+1/(x^4))	−2/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 2/x-2/(x^3)+1/(x^4)
d()/d(x)1/(2√(,x))	−1/(4*x√(,x))	Find the Derivative - d/dx 1/(2 square root of x)
d()/d(x)*(√(,x)+9/√(,x))	1/(2√(,x))−9/(2*x√(,x))	Find the Derivative - d/dx square root of x+9/( square root of x)
d(tan(3*x))/d(x)	3sec^2(3x)	Find the Derivative - d/dx tan(3x)
(lim_x→0^+)(x)*ln(x)	0	Evaluate Using L'Hospital's Rule
(∫_1^4)(√(,x)*d(x))	14/3	Evaluate the Integral
(∫_^)(9x^2+2x−9*d(x))	3x^3+x^2−9x+C	Evaluate the Integral integral of 9x^2+2x-9 with respect to x
(∫_^)((x^2)/(1+x^2)*d(x))	x−arctan(x)+C	Evaluate the Integral
(∫_^)(6xd(x))	3*x^2+C	Evaluate the Integral integral of 6x with respect to x
(∫_^)((2x+6)^5d(x))	((2*x+6)^6)/12+C	Evaluate the Integral integral of (2x+6)^5 with respect to x
(∫_^)((x^2−9)^3(2x)*d(x))	((x^2−9)^4)/4+C	Evaluate the Integral
ƒ(x)=5/(x^2+5)	(30*x^2−50)/((x^2+5)^3)	Find the 2nd Derivative f(x)=5/(x^2+5)
d^2()/(d(x)^2)√(,x+2)	−1/(4*(x+2)^(3/2))	Find the 2nd Derivative y = square root of x+2
(∫_0^2)(x^2*d(x))	8/3	Evaluate the Integral
(∫_^)(e^(−3t)d(t))	−1/3e^(−3t)+C	Evaluate the Integral integral of e^(-3t) with respect to t
(∫_^)(e^sin(x)cos(x)d(x))	e^sin(x)+C	Evaluate the Integral
(∫_^)(te^(−2t)*d(t))	−1/4e^(−2t)(2t+1)+C	Evaluate the Integral integral of te^(-2t) with respect to t
(∫_^)(ln(x)/√(,x)*d(x))	2√(,x)*ln(x)−4√(,x)+C	Evaluate the Integral
(∫_^)(2sin(x)d(x))	−2*cos(x)+C	Evaluate the Integral integral of 2sin(x) with respect to x
(∫_^)(√(,2x)d(x))	(2√(,2))/3*x^(3/2)+C	Evaluate the Integral
(∫_^)(xe^(−3x)*d(x))	−1/3xe^(−3x)−1/9e^(−3*x)+C	Evaluate the Integral integral of xe^(-3x) with respect to x
(∫_−2^3)((x^2−3)*d(x))	−10/3	Evaluate the Integral
(∫_^)(3^x*d(x))	3^x/ln(3)+C	Evaluate the Integral integral of 3^x with respect to x
(∫_^)((6x^2−2x−7)/√(,x)*d(x))	12/5x^(5/2)−4/3x^(3/2)−14*x^(1/2)+C	Evaluate the Integral
(∫_^)(25x^(3/2)d(x))	10*x^(5/2)+C	Evaluate the Integral integral of 25x^(3/2) with respect to x
(∫_^)(cos(x^2)*d(x))	(∑_n=0^∞)(((−1)^nx^(4n+1))/((4n+1)(2*n)!))+C	Evaluate the Integral integral of cos(x^2) with respect to x
(∫_^)(ln(5x)d(x))	xln(5x)−x+C	Evaluate the Integral
(∫_^)(tan^5(x)*d(x))	tan^4(x)/4-tan^2(x)/2+ln(abs(sec(x)))+C	Evaluate the Integral
(∫_^)(4*d(x))	4*x+C	Evaluate the Integral integral of 4 with respect to x
(∫_1^7)(w^2ln(w)d(w))	343/3*ln(7)−38	Evaluate the Integral
(∫_0^π/8)(sin(2x)d(x))	(2−√(,2))/4	Evaluate the Integral
(∫_^)(18x^(1/2)d(x))	12*x^(3/2)+C	Evaluate the Integral integral of 18x^(1/2) with respect to x
(∫_^)(1/(x+1)*d(x))	ln(abs(x+1))+C	Evaluate the Integral
d()/d(x)(4x^2+7*x−ln(x))	8*x+7−1/x	Find the Derivative - d/dd d/(dx)*(4x^2)+7x- natural log of x
(∫_^)(2x+9d(x))	x^2+9*x+C	Evaluate the Integral integral of 2x+9 with respect to x
arcsec(√(,2))	π/4	Evaluate arcsec( square root of 2)
e^(1−20x+5x^2)	2	Find the Critical Points e^(1-20x+5x^2)
tan(x+y)=x	−sin^2(x+y)	Find dy/dx tan(x+y)=x
2x^3+x^2y−x*y^3=2	(y^3−2xy−6x^2)/(x^2−3x*y^2)	Find dy/dx 2x^3+x^2y-xy^3=2
(x+y)^3=x^3+y^3	−(2xy+y^2)/(x^2+2xy)	Find dy/dx (x+y)^3=x^3+y^3
x^4(x+y)=y^2(3*x−y)	(3y^2−5x^4−4x^3y)/(x^4−6xy+3*y^2)	Find dy/dx x^4(x+y)=y^2(3x-y)
x^2+x*y−y^2=4	(2x+y)/(2y−x)	Find dy/dx x^2+xy-y^2=4
12x^2−176x+484	4(3x - 11)(x - 11)	Factor 12x^2-176x+484
d()/d(x)(x^2ln(x))	x+2xln(x)	Find the Derivative - d/d@VAR f(x)=x^2 natural log of x
d()/d(x)√(,x−1)	1/(2√(,x−1))	Find the Derivative - d/dx f(x) = square root of x-1
d()/d(x)x/2	1/2	Find the Derivative - d/dx f(x)=x/2
d()/d(x)*(x^2−1)	2*x	Find the Derivative - d/dx f(x)=x^2-1
d(√(,x^2+1))/d(x)	x/√(,x^2+1)	Find the Derivative - d/dx f(x) = square root of x^2+1
(d(4)*x^2)/d(x)	8*x	Find the Derivative - d/dx f(x)=4x^2
d()/d(x)x^2ln(x)	x+2xln(x)	Find the Derivative - d/dx f(x)=x^2 natural log of x
d()/d(x)7/√(,x)	−7/(2*x√(,x))	Find the Derivative - d/dx y=7/( square root of x)
d()/d(x)((x+6)*x)/(x+1)	(x^2+2*x+6)/((x+1)^2)	Find the Derivative - d/dx ((x+6)x)/(x+1)
(d(x^3)*e^x)/d(x)	x^2e^x(x+3)	Find the Derivative - d/dx x^3e^x
d(ln(3e^(2x−5)(3x^3+5)^7))/d(x)	2+(63x^2)/(3x^3+5)	Find the Derivative - d/dx natural log of 3e^(2x-5)(3x^3+5)^7
d(ln(x√(,x^2−1)))/d(x)	(2x^2−1)/(x(x^2−1))	Find the Derivative - d/dx natural log of x square root of x^2-1
(d(x)*ln(x))/d(x)	1+ln(x)	Find the Derivative - d/dx f(x)=x natural log of x
d(ln(√(,x)))/d(x)	1/(2*x)	Find the Derivative - d/dx f(x) = natural log of square root of x
(d(x^2)*y^2)/d(x)	2xy^2+2x^2yd(y)/d(x)	Find the Derivative - d/dx x^2y^2
d(ln(x))/d(x)	1/x	Find the Derivative of the natural log of x with respect to x
(d(x)√(,1−x^2))/d(x)	(1−2*x^2)/√(,1−x^2)	Find the Derivative - d/dx x square root of 1-x^2
d()/d(x)x^2sin(x)	x^2cos(x)+2x*sin(x)	Find the Derivative - d/dx y=x^2sin(x)
d(sec(x))/d(x)	3sec(x)tan(x)	Find the Derivative - d/dx sec(x)^3
(d(4)*cos(x))/d(x)	−4*sin(x)	Find the Derivative - d/dx 4cos(x)
d()/d(x)(x^2)/2	x	Find the Derivative - d/dx (x^2)/2
d((log_2)(x))/d(x)	1/(x*ln(2))	Find the Derivative - d/dx log base 2 of x
d()/d(x)(2x−3)^4*(x^2+x+1)^5	(2x−3)^3(x^2+x+1)^4(28x^2−12*x−7)	Find the Derivative - d/dx (2x-3)^4(x^2+x+1)^5
d()/d(x)1/(x^2)	−2/(x^3)	Find the Derivative Using Quotient Rule - d/dx 1/(x^2)
(∫_^)(7*d(x))	7*x+C	Evaluate the Integral integral of 7 with respect to x
(∫_^)(e^(−3t)d(t))	−1/3e^(−3t)+C	Find the Integral e^(-3t)
(∫_^)(e^(−x^2)*d(x))	√(,π)/2*erf(x)+C	Find the Integral e^(-x^2)
d()/d(r)*(√(,r)+√(5,R))	1/(2√(,r))	Find the Derivative - d/dr square root of r+ fifth root of R
d(ln(8))/d(I)	0	Find the Derivative - d/dI natural log of 8
d()/d(x)*(x^2+x)	2*x+1	Find the Derivative - d/d@VAR f(x)=x^2+x
d()/d(x)4x^2	8*x	Find the Derivative - d/d@VAR f(x)=4x^2
d()/d(x)6x^2	12*x	Find the Derivative - d/d@VAR f(x)=6x^2
d()/d(x)1/√(,x)	−1/(2*x√(,x))	Find the Derivative - d/d@VAR f(x)=1/( square root of x)
d(2*x+7)/d(x)	4(2x+7)	Find the Derivative - d/dx (2x+7)^2
d()/d(x)*x^7	7*x^6	Find the Derivative - d/dx y=x^7
d()/d(x)*(−csc(x)−cos(x))	csc(x)*cot(x)+sin(x)	Find the Derivative - d/dx -csc(x)-cos(x)
d()/d(x)cos(x)/(x^3)	(−xsin(x)−3cos(x))/(x^4)	Find the Derivative - d/dx (cos(x))/(x^3)
d(a^x)/d(x)	a^x*ln(a)	Find the Derivative - d/dx a^x
d()/d(x)(10−cos(x))/(10+sin(x))	(10sin(x)−10cos(x)+1)/((10+sin(x))^2)	Find the Derivative - d/dx (10-cos(x))/(10+sin(x))
d()/d(x)9/(8*x^2)	−9/(4*x^3)	Find the Derivative - d/dx 9/(8x^2)
d(√(,1−4*x))/d(x)	−2/√(,1−4*x)	Find the Derivative - d/dx square root of 1-4x
d(ln(8*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 8x
d()/d(x)*(x^2+y^2)	2x+2yd(y)/d(x)	Find the Derivative - d/dx x^2+y^2
d()/d(x)ln(x)/(x^2)	(1−2*ln(x))/(x^3)	Find the Derivative - d/dx ( natural log of x)/(x^2)
d()/d(x)7√(,x)sin(x)	(7sin(x))/(2√(,x))+7√(,x)cos(x)	Find the Derivative - d/dx 7 square root of xsin(x)
d()/d(x)−3	0	Find the Derivative - d/dx -3
d()/d(x)(2x)/(3y)	(2y−2xd(y)/d(x))/(3*y^2)	Find the Derivative - d/dx (2x)/(3y)
d(e^u)/d(u)	e^u	Find the Derivative - d/du e^u
1−1/95*x^2=0	±√(,95)	Solve for x 1-1/95x^2=0
(log_)(32⋅64)	(log_)(32)+(log_)(64)	Expand the Logarithmic Expression log of 32*64
y=ln(x^2+1)	ln(x^2+1)	Graph natural log of x^2+1
(lim_x→0)(sin(3*x)/x)	3	Evaluate the Limit ( limit as x approaches 0 of sin(3x))/x
(lim_x→4)((√(,x+5)−3)/(x−4))	1/6	Evaluate the Limit
y=2x−x^2,y=2x−4	32/3	Find the Area Between the Curves y=2x-x^2 , y=2x-4
(lim_x→1)(x)	1	Evaluate the Limit limit as x approaches 1 of x
(lim_x→2)((x−2)/(x−2))	1	Evaluate the Limit limit as x approaches 2 of (x-2)/(x-2)
(lim_x→0)(x/x)	1	Evaluate the Limit limit as x approaches 0 of x/x
(lim_x→4)((x^2−16)/(x−4))	8	Evaluate the Limit
(lim_x→1)(√(,x−1)/(x−1))	∞	Evaluate the Limit
(lim_x→5)((x−5)/(x^2−25))	1/10	Evaluate the Limit
(∫_^)(3x^2d(x))	x^3+C	Find the Antiderivative 3x^2
(∫_^)(sec^2(x)*d(x))	tan(x)+C	Find the Antiderivative sec(x)^2
(∫_^)(2x^2d(x))	(2*x^3)/3+C	Find the Antiderivative 2x^2
ƒ(x)=e^(1−20x+5x^2)	see full solution →	Find the Local Maxima and Minima f(x)=e^(1-20x+5x^2)
ƒ(x)=x^3−12*x+2	see full solution →	Find the Local Maxima and Minima f(x)=x^3-12x+2
ƒ(x)=x^2*e^(−x)	see full solution →	Find the Local Maxima and Minima f(x)=x^2e^(-x)
ƒ(x)=x+9/x	see full solution →	Find the Local Maxima and Minima f(x)=x+9/x
(lim_x→8)(e^(−x))	e^(−8)	Evaluate the Limit limit as x approaches 8 of e^(-x)
(lim_x→∞)(√(,9x^2+x)−3x)	1/6	Evaluate the Limit
(lim_x→∞)(e^(−x))	0	Evaluate the Limit limit as x approaches infinity of e^(-x)
(lim_x→9)((x−9)/(√(,x)−3))	6	Evaluate the Limit
(lim_x→16)((4−√(,x))/(16*x−x^2))	1/128	Evaluate the Limit
(lim_x→0)(sin(x)/(5*x))	1/5	Evaluate the Limit limit as x approaches 0 of (sin(x))/(5x)
F(x)=1/x	1/x	Graph F(x)=1/x
ƒ(x)=x^3−3*x^2	0, 2	Find the Critical Points f(x)=x^3-3x^2
ƒ(x)=2x^3+3x^2−12*x	see full solution →	Find Where Increasing/Decreasing Using Derivatives f(x)=2x^3+3x^2-12x
x^2+y^2=25	5, y = -5	Find the Horizontal Tangent Line x^2+y^2=25
x^2+y^2=−4*x	2, y = -2	Find the Horizontal Tangent Line x^2+y^2=-4x
(∫_0^2π)(cos(x)d(x))	0	Evaluate the Integral
(lim_x→0)((√(,x+4)−2)/x)	1/4	Evaluate the Limit
(∫_^)(((6+e^x)^2)/(e^x)*d(x))	−36e^(−x)+12x+e^x+C	Evaluate the Integral
(lim_x→0)(ƒ(x))	ƒ(0)	Evaluate the Limit limit as x approaches 0 of f(x)
d()/d(x)(∫_^)(e^(2x)*d(x))	e^(2*x)	Find the Derivative of the Integral integral of e^(2x) with respect to x
d()/d(x)(∫_0^10)((4x^2+7)*d(x))	0	Find the Derivative of the Integral
(∫_1^4)(3xd(x))	45/2	Evaluate the Integral
(∫_1^8)(1/(x^2)*d(x))	7/8	Evaluate the Integral
(∫_^)((x^3)/√(,x^2+36)*d(x))	((x^2−72)√(,x^2+36))/3+C	Evaluate the Integral
(∫_3^4)(x√(,x−3)*d(x))	12/5	Evaluate the Integral
(∫_4^5)(x√(,x−4)*d(x))	46/15	Evaluate the Integral
(∫_^)((x^2)/(x−1)*d(x))	1/2*x^2+x+ln(abs(x-1))+C	Evaluate the Integral
(∫_0^1)(√(,x)*d(x))	2/3	Evaluate the Integral
(∫_0^2)(5x^2d(x))	40/3	Evaluate the Integral
(∫_^)(1*d(t))	t+C	Evaluate the Integral integral of 1 with respect to t
(∫_^)(t^3e^(−t^2)d(t))	−1/2e^(−t^2)(t^2+1)+C	Evaluate the Integral
(∫_^)(πsin(πx)*d(x))	−cos(π*x)+C	Evaluate the Integral integral of pisin(pix) with respect to x
(∫_^)(20x^(3/2)d(x))	8*x^(5/2)+C	Evaluate the Integral integral of 20x^(3/2) with respect to x
(∫_^)(e^(8x)d(x))	(e^(8*x))/8+C	Evaluate the Integral integral of e^(8x) with respect to x
(∫_^)(x√(,x−1)*d(x))	2/5(x−1)^(5/2)+2/3(x−1)^(3/2)+C	Evaluate the Integral
(∫_^)(xsin^3(x)d(x))	see full solution →	Evaluate the Integral integral of xsin(x)^3 with respect to x
(∫_^)(9x^(1/2)d(x))	6*x^(3/2)+C	Evaluate the Integral integral of 9x^(1/2) with respect to x
(∫_^)(8e^(4y)*d(y))	2e^(4y)+C	Evaluate the Integral integral of 8e^(4y) with respect to y
(∫_0^1)(x^2*d(x))	1/3	Evaluate the Integral
(∫_^)((x^2+9x)cos(x)*d(x))	(x^2+9x−2)sin(x)+(2x+9)cos(x)+C	Evaluate the Integral
(∫_^)(x/((1−x^2)^3)*d(x))	1/(4*(1−x^2)^2)+C	Evaluate the Integral
(∫_^)(x^2√(,x^3+2)*d(x))	2/9*(x^3+2)^(3/2)+C	Evaluate the Integral
(∫_^)(x√(,x−5)*d(x))	2/5(x−5)^(5/2)+10/3(x−5)^(3/2)+C	Evaluate the Integral
(∫_^)((x^2)/√(,9−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_^)(e^(7x)d(x))	(e^(7*x))/7+C	Evaluate the Integral integral of e^(7x) with respect to x
(∫_^)(√(,16−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_^)(−sin(x)*d(x))	cos(x)+C	Evaluate the Integral integral of -sin(x) with respect to x
(∫_^)(1/(x^9)*d(x))	−1/(8*x^8)+C	Evaluate the Integral integral of 1/(x^9) with respect to x
(∫_0^1)((r^3)/√(,4+r^2)*d(r))	(16−7√(,5))/3	Evaluate the Integral
(∫_^)(1/(√(,x)(1+√(,x)))d(x))	2*ln(1+√(,x))+C	Evaluate the Integral
(∫_^)(1/(3−2x)d(x))	-1/2ln(abs(3-2x))+C	Evaluate the Integral
y=√(,x+7)	−1/(4*(x+7)^(3/2))	Find the 2nd Derivative y = square root of x+7
ƒ(x)=√(,x^2+7)	7/((x^2+7)√(,x^2+7))	Find the 2nd Derivative f(x) = square root of x^2+7
ƒ(x)=x/(x^2+1)	(2x(x^2−3))/((x^2+1)^3)	Find the 2nd Derivative f(x)=x/(x^2+1)
(∫_^)((x+1)e^(4x^2+8x)d(x))	1/8e^(4x^2+8*x)+C	Evaluate the Integral
(∫_64^8)(ln(y)/√(,y)*d(y))	12√(,2)ln(2)−8√(,2)−96ln(2)+32	Evaluate the Integral
(∫_^)((3x+2)^2d(x))	3x^3+6x^2+4*x+C	Evaluate the Integral integral of (3x+2)^2 with respect to x
(∫_^)(ln(x)/x*d(x))	ln(x)/4+C	Evaluate the Integral
d(√(,x^2+10))/d(x)	x/√(,x^2+10)	Find the Derivative - d/dx square root of x^2+10
d()/d(x)(−5)/(x^2)	10/(x^3)	Find the Derivative - d/dx -5/(x^2)
d^2(e^(−x^2))/(d(x)^2)	(4x^2−2)e^(−x^2)	Find the 2nd Derivative e^(-x^2)
d^2(e^x)/(d(x)^2)	e^x	Find the 2nd Derivative e^x
d(√(,2−6*x))/d(x)	(−3)/√(,2−6*x)	Find the Derivative - d/dx square root of 2-6x
d(4*x+1)/d(x)	8(4x+1)	Find the Derivative - d/dx (4x+1)^2
(lim_x→8)(x)*e^(−x)	8/(e^8)	Evaluate the Limit limit as x approaches 8 of xe^(-x)
(lim_x→0)(x/x)	1	Evaluate the Limit as x approaches 0 of x/x
ƒ(x)=x*ln(x)	see full solution →	Find the Local Maxima and Minima f(x)=x natural log of x
d()/d(x)(x^2−1)/(x^2+1)	(4*x)/((x^2+1)^2)	Find the Derivative - d/dx (x^2-1)/(x^2+1)
ƒ(x)=x^3−3*x^2+1	see full solution →	Find the Local Maxima and Minima f(x)=x^3-3x^2+1
(lim_x→1)((x^3−1)/(x^2−1))	3/2	Evaluate the Limit
ƒ(x)=x^4−4*x^3	Local Minimum: *(3,−27), Local Maxima: None	Find the Local Maxima and Minima f(x)=x^4-4x^3
ƒ(x)=ln(x)/x	see full solution →	Find the Local Maxima and Minima f(x)=( natural log of x)/x
(∫_^)(1*d(x))	x+C	Find the Antiderivative 1
(lim_x→−2)((x^3+8)/(x+2))	12	Evaluate the Limit
(lim_x→1)((x^4−1)/(x−1))	4	Evaluate the Limit
(lim_x→2)((x^3−8)/(x−2))	12	Evaluate the Limit
(lim_x→2)((x−2)/(x−2))	1	Evaluate the Limit limit as x approaches 2 of (x-2)/(x-2)
(lim_x→−4)((√(,x^2+9)−5)/(x+4))	−4/5	Evaluate the Limit
(lim_h→0)((√(,9+h)−3)/h)	1/6	Evaluate the Limit
(lim_x→0)(1)	1	Evaluate the Limit limit as x approaches 0 of 1
(lim_x→0)(sin(1/x))	Does Not Exist	Evaluate the Limit limit as x approaches 0 of sin(1/x)
(lim_x→2)(x)	2	Evaluate the Limit limit as x approaches 2 of x
(lim_x→36)((√(,x)−6)/(x−36))	1/12	Evaluate the Limit
(lim_x→2)((x−2)/(x^2−4))	1/4	Evaluate the Limit limit as x approaches 2 of (x-2)/(x^2-4)
(lim_x→2)(2)	2	Evaluate the Limit limit as x approaches 2 of 2
y=x,y=√(,x)	1/6	Find the Area Between the Curves y=x , y = square root of x
(lim_h→0)(((2+h)^3−8)/h)	12	Evaluate the Limit
y=2x^3−5x,(1,−3)	x−4	Find the Tangent Line at the Point y=2x^3-5x , (1,-3)
ln(sec(x)+tan(x))	ln(sec(x)+tan(x))	Graph natural log of sec(x)+tan(x)
y=ln(5*x)	ln(5*x)	Graph natural log of 5x
3^(x−5)=7^(2*x)	(5*ln(3))/(ln(3)−ln(49))	Solve for x 3^(x-5)=7^(2x)
(3+h)^3	27+27h+9h^2+h^3	Simplify (3+h)^3
d()/d(x)2/(x+1)	−2/((x+1)^2)	Find the Derivative - d/dx 2/(x+1)
d()/d(x)(4x−7)^2	32*x−56	Find the Derivative - d/dx (4x-7)^2
d()/d(x)1/(x^2−1)	(−2*x)/((x^2−1)^2)	Find the Derivative - d/dx 1/(x^2-1)
d()/d(x)1/(2*x+1)	−2/((2*x+1)^2)	Find the Derivative - d/dx 1/(2x+1)
d()/d(x)1/(x+3)	−1/((x+3)^2)	Find the Derivative - d/dx 1/(x+3)
d()/d(x)8e^x*cos(x)	8e^x(cos(x)−sin(x))	Find the Derivative - d/dx 8e^xcos(x)
d()/d(x)(x^2)/y	(2xy−x^2d(y)/d(x))/(y^2)	Find the Derivative - d/dx (x^2)/y
d()/d(x)*2^7⋅0	0	Find the Derivative - d/dx 2^7*0
d()/d(x)*(e^x−e^(−x))	e^x+e^(−x)	Find the Derivative - d/dx e^x-e^(-x)
d(e^(1−x))/d(x)	−e^(1−x)	Find the Derivative - d/dx e^(1-x)
d(e^(x/2))/d(x)	1/2*e^(x/2)	Find the Derivative - d/dx e^(x/2)
d()/d(x)(8x+1)^2	128*x+16	Find the Derivative - d/dx (8x+1)^2
d()/d(x)*(x^2+x−3)	2*x+1	Find the Derivative - d/dx x^2+x-3
d()/d(x)(x^3)/3	x^2	Find the Derivative - d/dx (x^3)/3
d(4*x+5)/d(x)	32*x+40	Find the Derivative - d/dx (4x+5)^2
d()/d(x)x/(x^2+16)	(16−x^2)/((x^2+16)^2)	Find the Derivative - d/dx x/(x^2+16)
d(x^(1/x))/d(x)	x^(1/x)*((1−ln(x))/(x^2))	Find the Derivative - d/dx x^(1/x)
d()/d(x)((x+9)*x)/(x+1)	(x^2+2*x+9)/((x+1)^2)	Find the Derivative - d/dx y=((x+9)x)/(x+1)
d()/d(x)x^2cos(x)	2xcos(x)−x^2*sin(x)	Find the Derivative - d/dx x^2cos(x)
d()/d(x)x^2(1−5*x)	2x−15x^2	Find the Derivative - d/dx x^2(1-5x)
d()/d(x)*4√(,x+18)	2/√(,x+18)	Find the Derivative - d/dx 4 square root of x+18
d()/d(x)*(1+ln(x))	1/x	Find the Derivative - d/dx 1+ natural log of x
d()/d(x)cot(x)/sin(x)	−(1+cos^2(x))/sin^3(x)	Find the Derivative - d/dx (cot(x))/(sin(x))
d(x^7)/d(x)	7*x^6	Find the Derivative - d/d@VAR f(x)=x^7
(∫_^)(e^(−5x)d(x))	−1/5e^(−5x)+C	Evaluate the Integral integral of e^(-5x) with respect to x
d()/d(x)*(x^2+x−3)	2*x+1	Find the Derivative - d/d@VAR f(x)=x^2+x-3
d(sin(x))/d(x)	cos(x)	Find the Derivative - d/d@VAR f(x)=sin(x)
d()/d(x)*(x^2−5)	2*x	Find the Derivative - d/d@VAR f(x)=x^2-5
(√(,x+h+5)−√(,x+5))/h	1/(√(,x+h+5)+√(,x+5))	Simplify
(∫_^)(1/(2x)d(x))	1/2*ln(abs(x))+C	Evaluate the Integral
d()/d(x)x^2(1−3*x)	2x−9x^2	Find the Derivative - d/dx x^2(1-3x)
d()/d(y)1/y	−1/(y^2)	Find the Derivative - d/dy 1/y
d()/d(Z)1/8	0	Find the Derivative - d/dZ 1/8
d()/d(x)(−x+1)/(x+1)	−2/((x+1)^2)	Find the Derivative - d/dx -x+1/x+1
d()/d(x)*cos(cos(cos(x)))	−sin(cos(cos(x)))⋅sin(cos(x))⋅sin(x)	Find the Derivative - d/dx y=cos(cos(cos(x)))
d(3*x+1)/d(x)	6(3x+1)	Find the Derivative - d/dx (3x+1)^2
d()/d(x)sin(x)/x	(x*cos(x)−sin(x))/(x^2)	Find the Derivative - d/dx y=(sin(x))/x
d()/d(x)(2x^2−9*x+10)	4*x−9	Find the Derivative - d/dx 2x^2-9x+10
d()/d(x)1/2*x^2√(,25−x^2)	(50x−3x^3)/(2√(,25−x^2))	Find the Derivative - d/dx 1/2x^2 square root of 25-x^2
d(sin(x^2))/d(x)	2xcos(x^2)	Find the Derivative - d/dx f(x)=sin(x^2)
d(ln(x+3))/d(x)	1/(x+3)	Find the Derivative - d/dx natural log of x+3
d(x^12)/d(x)	12*x^11	Find the Derivative - d/dx x^12
d()/d(x)((x^2−2)^(3/2))/3	x√(,x^2−2)	Find the Derivative - d/dx ((x^2-2)^(3/2))/3
d()/d(x)8/(x^2+4)	−(16*x)/((x^2+4)^2)	Find the Derivative - d/dx 8/(x^2+4)
d()/d(x)*1	0	Find the Derivative - d/dx f(x)=1
d()/d(x)*3	0	Find the Derivative - d/dx f(x)=3
(∫_^)(cot(x)*d(x))	ln(abs(sin(x)))+C	Evaluate the Integral
d(e^(x^2))/d(x)	2xe^(x^2)	Find the Derivative - d/dx f(x)=e^(x^2)
d()/d(x)sin(x)/(x^2)	(xcos(x)−2sin(x))/(x^3)	Find the Derivative - d/dx (sin(x))/(x^2)
(d(x^2)*e^x)/d(x)	x^2e^x+2x*e^x	Find the Derivative - d/dx f(x)=x^2e^x
(∫_^)(1/√(,x)*d(x))	2√(,x)+C	Find the Integral 1/( square root of x)
x^2y+xy^2=6	−(2xy+y^2)/(x^2+2xy)	Find dy/dx x^2y+xy^2=6
x^3*y^3−y=x	(1−3x^2y^3)/(3x^3y^2−1)	Find dy/dx x^3y^3-y=x
x^3−x*y+y^2=4	(y−3x^2)/(2y−x)	Find dy/dx x^3-xy+y^2=4
1/x+1/y=1	−(y^2)/(x^2)	Find dy/dx 1/x+1/y=1
√(,xy)=x−2y	(2√(,xy)−y)/(x+4√(,xy))	Find dy/dx square root of xy=x-2y
d()/d(x)2/x	−2/(x^2)	Find the Derivative - d/d@VAR f(x)=2/x
x*y+x=2	−(y+1)/x	Find dy/dx xy+x=2
x*y=4	−y/x	Find dy/dx xy=4
2(x^2+y^2)^2=25(x^2−y^2)	(25x−4x(x^2+y^2))/(4y(x^2+y^2)+25y)	Find dy/dx 2(x^2+y^2)^2=25(x^2-y^2)
2x^2−3y^2=4	(2x)/(3y)	Find dy/dx 2x^2-3y^2=4
1−x*y=x−y	(1+y)/(1−x)	Find dy/dx 1-xy=x-y
d()/d(x)√(,x)	1/(2√(,x))	Find dy/dx y = square root of x
d()/d(x)(x+9)(x^2−9)	3x^2+18x−9	Find the Derivative - d/dx (x+9)(x^2-9)
d()/d(x)(4*x)/(x^2+1)	(4−4*x^2)/((x^2+1)^2)	Find the Derivative - d/dx (4x)/(x^2+1)
d()/d(x)*(2^8⋅0)	0	Find the Derivative - d/dx 2^8*0
(d(7)*sin(x))/d(x)	7*cos(x)	Find the Derivative - d/dx 7sin(x)
d()/d(x)*2^9⋅0	0	Find the Derivative - d/dx 2^9*0
d()/d(t)(at^2+b*t+c)	2at+b	Find the Derivative - d/dt at^2+bt+c
d^2(e^(x^2))/(d(x)^2)	2e^(x^2)(2*x^2+1)	Find the 2nd Derivative e^(x^2)
d()/d(x)[(x^6+x)(x^6−x)]	12x^11−2x	Find the Derivative - d/dx [(x^6+x)(x^6-x)]
(∫_^)((−x^8+4)^6x^7d(x))	−((−x^8+4)^7)/56+C	Evaluate the Integral
(∫_^)((7x^5+7x^2+14)/(x^3−x)*d(x))	see full solution →	Evaluate the Integral
ƒ(x)=√(,x)	−1/(4*x√(,x))	Find the 2nd Derivative f(x) = square root of x
ƒ(x)=√(,x^2+20)	20/√(,(x^2+20)^3)	Find the 2nd Derivative f(x) = square root of x^2+20
ƒ(x)=√(,x^2+21)	21/((x^2+21)√(,x^2+21))	Find the 2nd Derivative f(x) = square root of x^2+21
ƒ(x)=√(,x^2+12)	12/((x^2+12)√(,x^2+12))	Find the 2nd Derivative f(x) = square root of x^2+12
ƒ(x)=√(,x^2+9)	9/((x^2+9)^(3/2))	Find the 2nd Derivative f(x) = square root of x^2+9
(∫_^)(ln(2x)d(x))	xln(2x)−x+C	Evaluate the Integral
(∫_^)(ln(x^2)*d(x))	2xln(x)−2*x+C	Evaluate the Integral
(∫_^)(cos(2x)/(1+sin(2x))*d(x))	1/2ln(abs(1+sin(2x)))+C	Evaluate the Integral
(∫_^)(e^(−t)*d(t))	−e^(−t)+C	Evaluate the Integral integral of e^(-t) with respect to t
(∫_^)((4x^2)/(x^2+9)d(x))	4x−12arctan(x/3)+C	Evaluate the Integral
(∫_^)(sin(ln(x))*d(x))	(x*(sin(ln(x))−cos(ln(x))))/2+C	Evaluate the Integral
(∫_^)(x^9*d(x))	(x^10)/10+C	Evaluate the Integral integral of x^9 with respect to x
(∫_^)(9/√(,x)*d(x))	18√(,x)+C	Evaluate the Integral
(∫_0^1)((x^2+7)e^(−x)d(x))	9−12/e	Evaluate the Integral
(∫_^)(3/(x^2)*d(x))	−3/x+C	Evaluate the Integral integral of 3/(x^2) with respect to x
(∫_^)(cos(x)/sin^2(x)*d(x))	−csc(x)+C	Evaluate the Integral
(∫_−1^1)(1/(1+y^2)*d(y))	π/2	Evaluate the Integral
(∫_−1^1)((4x^2−1)(x+3)*d(x))	2	Evaluate the Integral
(∫_^)(csc^3(x)*d(x))	see full solution →	Evaluate the Integral integral of csc(x)^3 with respect to x
(∫_^)(((ln(x))^2)/(x^3)*d(x))	−(2(ln(x))^2+2ln(x)+1)/(4*x^2)+C	Evaluate the Integral
(∫_1^2)((e^1/(x^3))/(x^4)*d(x))	(e−√(8,e))/3	Evaluate the Integral
(∫_0^1)(x/((x^2+1)^3)*d(x))	3/16	Evaluate the Integral
(∫_0^3)(√(,9−x^2)*d(x))	(9*π)/4	Evaluate the Integral
(∫_^)(3√(,x)*d(x))	2*x^(3/2)+C	Evaluate the Integral
(∫_^)(4/x*d(x))	4*ln(x)	Evaluate the Integral
(∫_^)(√(,6x+5)d(x))	1/9(6x+5)^(3/2)+C	Evaluate the Integral
(∫_^)(x^8ln(x)d(x))	(x^9*ln(x))/9−(x^9)/81+C	Evaluate the Integral
(∫_36^4)((9ln(y))/√(,y)d(y))	144−144ln(2)−216ln(3)	Evaluate the Integral
(∫_^)((x+1)/(x^2+2x)d(x))	1/2ln(abs(x^2+2x))+C	Evaluate the Integral
(∫_^)((x^2+5x)cos(x)*d(x))	(x^2+5x−2)sin(x)+(2x+5)cos(x)+C	Evaluate the Integral
(∫_^)(xcos(x)d(x))	x*sin(x)+cos(x)+C	Evaluate the Integral integral of xcos(x) with respect to x
(∫_0^1)(x*d(x))	1/2	Evaluate the Integral
(∫_^)(x√(,x^2+4)*d(x))	1/3*(x^2+4)^(3/2)+C	Evaluate the Integral
(∫_^)(te^(−7t)*d(t))	−1/7te^(−7t)−1/49e^(−7*t)+C	Evaluate the Integral integral of te^(-7t) with respect to t
(∫_^)(te^(−8t)*d(t))	−1/8te^(−8t)−1/64e^(−8*t)+C	Evaluate the Integral integral of te^(-8t) with respect to t
(∫_0^8)(e^(−x)*d(x))	1−e^(−8)	Evaluate the Integral
(∫_^)(2e^(5x)*d(x))	2/5e^(5x)+C	Evaluate the Integral integral of 2e^(5x) with respect to x
(∫_0^4)(4x^2d(x))	256/3	Evaluate the Integral
(∫_0^4)(5x^2d(x))	320/3	Evaluate the Integral
(∫_0^4)(x*d(x))	8	Evaluate the Integral
(∫_^)(e^(2y)d(y))	(e^(2*y))/2+C	Evaluate the Integral integral of e^(2y) with respect to y
(∫_-1^2)(x*d(x))	3/2	Evaluate the Integral
(∫_^)(cos(7x)d(x))	1/7sin(7x)+C	Evaluate the Integral integral of cos(7x) with respect to x
(∫_1^4)(1/x*d(x))	ln(4)	Evaluate the Integral
(∫_^)(x^8*d(x))	(x^9)/9+C	Evaluate the Integral integral of x^8 with respect to x
(∫_−1^0)(t^(1/3)−t^(2/3)*d(t))	−27/20	Evaluate the Integral
d(ln(x^3))/d(x)	3/x	Find the Derivative - d/dx natural log of x^3
(lim_x→0)((√(,x+5)−√(,5))/x)	√(,5)/10	Evaluate the Limit
(∫_^)((4x)/(x^2+9)d(x))	2*ln(x^2+9)+C	Evaluate the Integral
(∫_^)(x^3e^(2x)*d(x))	see full solution →	Evaluate the Integral integral of x^3e^(2x) with respect to x
sin(5)	sin(5)≈−0.95892427	Evaluate sin(5)
cos((7*π)/4)	√(,2)/2	Evaluate cos((7pi)/4)
arctan(−1/3)	−arctan(1/3)	Evaluate arctan(-1/3)
x^3−12*x	−2,2	Find the Critical Points x^3-12x
d()/d(x)*(3/x−2/(x^3)+1/(x^4))	−3/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 3/x-2/(x^3)+1/(x^4)
d()/d(x)√(,3x+2cos(x))	(3−2sin(x))/(2√(,3x+2*cos(x)))	Find the Derivative - d/dx y = square root of 3x+2cos(x)
d()/d(x)1/x	−1/(x^2)	Find dy/dx y=1/x
2*x^2+y^2=12	−(2*x)/y	Find dy/dx 2x^2+y^2=12
x^3+y^3=3xy	(y−x^2)/(y^2−x)	Find dy/dx x^3+y^3=3xy
x^3+y^3=5	−(x^2)/(y^2)	Find dy/dx x^3+y^3=5
x*y=1	−y/x	Find dy/dx xy=1
x=tan(y)	1/(1+x^2)	Find dy/dx x=tan(y)
x^2+y^2=100	−x/y	Find dy/dx x^2+y^2=100
x^3−x*y+y^2=7	(y−3x^2)/(2y−x)	Find dy/dx x^3-xy+y^2=7
(∫_0^1)((e^(2x)−e^(−2x))/(e^(2x)+e^(−2x))*d(x))	1/2*ln((e^2+e^(−2))/2)	Evaluate the Integral
x*y^2=4	−y/(2*x)	Find dy/dx xy^2=4
(∫_^)(2/x*d(x))	2*ln(x)	Evaluate the Integral
(∫_^)(e^y*d(y))	e^y+C	Find the Integral e^y
(∫_^)(arcsin(x)*d(x))	x*arcsin(x)+√(,1−x^2)+C	Find the Integral arcsin(x)
(∫_^)((ln(x))^2*d(x))	x(ln(x))^2−2xln(x)+2x+C	Find the Integral ( natural log of x)^2
d()/d(x)(x^2+2x)	2*x+2	Find the Derivative - d/d@VAR f(x)=x^2+2x
d()/d(x)(2x^2−5*x+3)	4*x−5	Find the Derivative - d/d@VAR f(x)=2x^2-5x+3
d(ln(x))/d(x)	1/x	Find the Derivative - d/d@VAR f(x) = natural log of x
d()/d(x)3/x	−3/(x^2)	Find the Derivative - d/d@VAR f(x)=3/x
d(√(,x+1))/d(x)	1/(2√(,x+1))	Find the Derivative - d/dx f(x) = square root of x+1
d(√(5,x))/d(x)	1/(5√(5,x^4))	Find the Derivative - d/dx f(x) = fifth root of x
d(e^(−2*x))/d(x)	−2e^(−2x)	Find the Derivative - d/dx f(x)=e^(-2x)
d()/d(x)*(4−x^2)	−2*x	Find the Derivative - d/dx f(x)=4-x^2
d()/d(x)2x^2	4*x	Find the Derivative - d/dx f(x)=2x^2
(d(cos(x))*sin(x))/d(x)	cos(2*x)	Find the Derivative - d/dx cos(x)sin(x)
d(cos(ln(x)))/d(x)	−sin(ln(x))/x	Find the Derivative - d/dx cos( natural log of x)
(d(4)*x^4)/d(x)	16*x^3	Find the Derivative - d/dx 4x^4
d()/d(x)6x*y	6y+6xd(y)/d(x)	Find the Derivative - d/dx 6xy
d()/d(x)1/(x^3)	−3/(x^4)	Find the Derivative - d/dx f(x)=1/(x^3)
d()/d(x)1/(x−1)	−1/((x−1)^2)	Find the Derivative - d/dx f(x)=1/(x-1)
d(ln(x−√(,x^2−1)))/d(x)	−1/√(,x^2−1)	Find the Derivative - d/dx natural log of x- square root of x^2-1
d(sin(tan(2*x)))/d(x)	2sec^2(2x)cos(tan(2x))	Find the Derivative - d/dx sin(tan(2x))
d()/d(x)*(x−ln(x))	1−1/x	Find the Derivative - d/dx x- natural log of x
d()/d(x)(x^2−3x+3)	2*x−3	Find the Derivative - d/dx x^2-3x+3
d()/d(x)*(5/x−2/(x^3)+1/(x^4))	−5/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 5/x-2/(x^3)+1/(x^4)
(d(x)*tan(x))/d(x)	x*sec^2(x)+tan(x)	Find the Derivative - d/dx xtan(x)
d()/d(x)*(sin(x)+cos(x))	cos(x)−sin(x)	Find the Derivative - d/dx f(x)=sin(x)+cos(x)
d(cot(x))/d(x)	−csc^2(x)	Find the Derivative - d/dx f(x)=cot(x)
d(ln(e^(2*x)))/d(x)	2	Find the Derivative - d/dx natural log of e^(2x)
d()/d(x)x^7e^x	x^6e^x(x+7)	Find the Derivative - d/dx y=x^7e^x
(d(5)*x^4)/d(x)	20*x^3	Find the Derivative - d/dx 5x^4
d()/d(x)(xsin(x)+cos(x))	x*cos(x)	Find the Derivative - d/dx xsin(x)+cos(x)
d(sin(x))/d(x)	5sin(x)cos(x)	Find the Derivative - d/dx sin(x)^5
d(4*x−6)/d(x)	32*x−48	Find the Derivative - d/dx (4x-6)^2
d()/d(x)ln(3x)	1/x	Find the Derivative - d/dx y = natural log of 3x
d()/d(x)4e^(x^2)	8xe^(x^2)	Find the Derivative - d/dx y=4ex^2
d()/d(x)e^(3x)cos(2x)	e^(3x)(3cos(2x)−2sin(2x))	Find the Derivative - d/dx e^(3x)cos(2x)
d()/d(x)(4x−9)^2	8(4x−9)	Find the Derivative - d/dx (4x-9)^2
(d(x^2)*y)/d(y)	x^2	Find the Derivative - d/dy x^2y
(∫_^)(x^(−3)*d(x))	−1/(2*x^2)+C	Find the Integral x^-3
(∫_^)(sin(x^2)*d(x))	see full solution →	Find the Integral sin(x^2)
(∫_^)(3x^2d(x))	x^3+C	Find the Integral 3x^2
(∫_^)(ln(x)/x*d(x))	((ln(x))^2)/2+C	Find the Integral ( natural log of x)/x
(∫_^)(√(3,x^2)*d(x))	(3*x^(5/3))/5+C	Find the Integral cube root of x^2
d()/d(t)(t^2ln(t))	2tln(t)+t	Evaluate the Integral
d()/d(t)(2t^2+t)	4*t+1	Find dx/dt x=2t^2+t
d(x)/d(t)* where x=3t	3	Find dx/dt x=3t
√(,x)/(x^2)	1/(x^(3/2))	Simplify ( square root of x)/(x^2)
√(,√(,b))/√(3,a*b)	1/(a^(1/3)*b^(1/12))	Simplify
d()/d(r)4π*r^2	8πr	Find the Derivative - d/dr 4pr^2
d(e^(−2*t))/d(t)	−2e^(−2t)	Find the Derivative - d/dt e^(-2t)
d()/d(x)3/(x^2)	−6/(x^3)	Find the Derivative - d/d@VAR f(x)=3/(x^2)
(d(2)e^(3x))/d(x)	6e^(3x)	Find the Derivative - d/dx 2e^(3x)
d()/d(x)(2x+5)^2	8*x+20	Find the Derivative - d/dx (2x+5)^2
d()/d(x)(x+3)/(x−1)	−4/((x−1)^2)	Find the Derivative - d/dx (x+3)/(x-1)
d()/d(x)(x+y)/(x−y)	(2xd(y)/d(x)−2y)/((x−y)^2)	Find the Derivative - d/dx (x+y)/(x-y)
d()/d(x)(√(,x)+x)/(x^2)	−3/(2*x^2√(,x))−1/(x^2)	Find the Derivative - d/dx ( square root of x+x)/(x^2)
d(x^n)/d(x)	n*x^(n−1)	Find the Derivative - d/dx x^n
d()/d(x)x/(x−2)	−2/((x−2)^2)	Find the Derivative - d/dx x/(x-2)
d(√(,x^2+2))/d(x)	x/√(,x^2+2)	Find the Derivative - d/dx square root of x^2+2
d()/d(x)(x^2+4x)	2*x+4	Find the Derivative - d/dx x^2+4x
d()/d(x)(−2)/(x^3)	6/(x^4)	Find the Derivative - d/dx -2/(x^3)
(d(8)*x^4)/d(x)	32*x^3	Find the Derivative - d/dx 8x^4
d()/d(x)7/√(,x)	−7/(2*x√(,x))	Find the Derivative - d/dx 7/( square root of x)
d()/d(x)2/√(4,x^3)	−3/(2*x^(7/4))	Find the Derivative - d/dx 2/( fourth root of x^3)
d(√(,x^2+8))/d(x)	x/√(,x^2+8)	Find the Derivative - d/dx square root of x^2+8
d(4*x−1)/d(x)	8(4x−1)	Find the Derivative - d/dx (4x-1)^2
d(e^(e^x))/d(x)	e^(e^x)*e^x	Find the Derivative - d/dx e^(e^x)
d()/d(x)2/√(,x)	−1/(x√(,x))	Find the Derivative - d/dx 2/( square root of x)
d()/d(x)8/x	−8/(x^2)	Find the Derivative - d/dx 8/x
d()/d(x)*(x−√(3,x))	1−1/(3√(3,x^2))	Find the Derivative - d/dx x- cube root of x
d()/d(x)sin(tan(7x))	7cos(tan(7x))sec^2(7x)	Find the Derivative - d/dx y=sin(tan(7x))
d(√(,x^2))/d(x)	x/√(,x^2)	Find the Derivative - d/dx square root of x^2
(d(x^2)*tan(x))/d(x)	x^2sec^2(x)+2x*tan(x)	Find the Derivative - d/dx x^2tan(x)
d(sin(cos(x)))/d(x)	−sin(x)*cos(cos(x))	Find the Derivative - d/dx sin(cos(x))
d(sin(e^x))/d(x)	e^x*cos(e^x)	Find the Derivative - d/dx sin(e^x)
d()/d(x)(e^(−x)+1)/(e^x)	−2e^(−2x)−e^(−x)	Find the Derivative - d/dx (e^(-x)+1)/(e^x)
d()/d(t)(2t^2+t)	4*t+1	Find the Derivative - d/dt 2t^2+t
d()/d(t)1/(t^2)	−2/(t^3)	Find the Derivative - d/dt 1/(t^2)
cot(x)	cos(x)/sin(x)	Simplify cot(x)
(x+h)^4	x^4+4x^3h+6x^2h^2+4xh^3+h^4	Simplify (x+h)^4
(x^(1/3))^2	x^(2/3)	Simplify (x^(1/3))^2
4x^3−16x=0	0, 2, -2	Solve for x 4x^3-16x=0
x=2√(,x)	0, 4	Solve for x x=2 square root of x
3−x^2=x−17	−5,4	Solve for x 3-x^2=x-17
3x^2−6x=0	0, 2	Solve for x 3x^2-6x=0
tan(x)=−1/3	see full solution →	Solve for x tan(x)=-1/3
(lim_x→0)((x^3+12x^2−5x)/(5*x))	−1	Evaluate the Limit
(∫_0^3)(81x-x^5)d(x)	243	Evaluate the Integral
(lim_x→2)(3)	3	Evaluate the Limit limit as x approaches 2 of 3
(lim_x→−2)(ƒ(x))	ƒ*(−2)	Evaluate the Limit limit as x approaches -2 of f(x)
(lim_x→2)(1/((x−2)^2))	∞	Evaluate the Limit limit as x approaches 2 of 1/((x-2)^2)
(lim_x→0)(sin^2(x)/x)	0	Evaluate the Limit limit as x approaches 0 of (sin(x)^2)/x
(lim_x→−1)((x^2−1)/(x+1))	−2	Evaluate the Limit
(lim_x→0)(x)*cos(1/x)	0	Evaluate the Limit limit as x approaches 0 of xcos(1/x)
(lim_x→−2)((x^2−4)/(x+2))	−4	Evaluate the Limit
(lim_x→−∞)(x+√(,x^2+2*x))	−1	Evaluate the Limit
(lim_x→0)(csc(x)−cot(x))	0	Evaluate the Limit limit as x approaches 0 of csc(x)-cot(x)
(lim_x→0)(1−2*x)	e^(−2)	Evaluate the Limit limit as x approaches 0 of (1-2x)^(1/x)
(lim_x→36)((√(,x)−6)/(x−36))	1/12	Evaluate the Limit
(lim_x→25)((√(,x)−5)/(x−25))	1/10	Evaluate the Limit
(lim_x→5)((x^2−25)/(x−5))	10	Evaluate the Limit
(lim_x→6)((x^2−36)/(x−6))	12	Evaluate the Limit
(lim_x→π/2)(cos(x)/(1−sin(x)))	Does Not Exist	Evaluate the Limit
(∫_^)(x^4*d(x))	(x^5)/5+C	Find the Antiderivative x^4
d(√(6,x^7))/d(x)	(7√(6,x))/6	Find the Derivative - d/dx sixth root of x^7
d(cos(ln(x)))/d(x)	−sin(ln(x))/x	Find the Derivative - d/d@VAR f(x)=cos( natural log of x)
d(√(,1−2*x))/d(x)	−1/√(,1−2*x)	Find the Derivative - d/d@VAR f(X) = square root of 1-2x
d()/d(x)5x^2	10*x	Find the Derivative - d/d@VAR f(x)=5x^2
ƒ(x)=(2x^2+3)/(4x^2+5)	see full solution →	Find the Local Maxima and Minima f(x)=(2x^2+3)/(4x^2+5)
ƒ(x)=2x^3−12x^2−72*x+2017	see full solution →	Find the Local Maxima and Minima f(x)=2x^3-12x^2-72x+2017
(lim_x→1)((x^3−1)/(x−1))	3	Evaluate the Limit limit as x approaches 1 of (x^3-1)/(x-1)
y=√(,x−4)/√(,x+4)	4/(√(,x−4)*(x+4)^(3/2))	Find dy/dx
(lim_x→5)(x^2)	25	Evaluate the Limit limit as x approaches 5 of x^2
(lim_x→8)(ƒ(x))	ƒ(8)	Evaluate the Limit limit as x approaches 8 of f(x)
ƒ(x)=tan((π*x)/2)	2*k+1,k∈ℤ	Find Where Undefined/Discontinuous f(x)=tan((pix)/2)
sec(π/3)	4	Evaluate sec(pi/3)^2
3x^(2/3)−2x	0, x = 1	Find the Critical Points 3x^(2/3)-2x
ƒ(x)=x^3−27*x	3, -3	Find the Critical Points f(x)=x^3-27x
cot(π)	undefined	Evaluate cot(pi)
tan(−1/3)	−tan(1/3)	Evaluate tan(-1/3)
tan(−4/5)	tan(−4/5)≈−1.029638557	Evaluate tan(-4/5)
tan((7*π)/6)	√(,3)/3	Evaluate tan((7pi)/6)
ƒ(x)=x/(x^2+1)	see full solution →	Find Where Increasing/Decreasing Using Derivatives f(x)=x/(x^2+1)
ƒ(x)=x^3−12*x	(0,0)	Find the Inflection Points f(x)=x^3-12x
d()/d(x)*(x^2−2)	2*x	Find the Derivative - d/dx x^2-2
(d(x^5)*e^x)/d(x)	x^4e^x(x+5)	Find the Derivative - d/dx x^5e^x
ƒ(x)=x/√(,2*x−1)	1	Find the Horizontal Tangent Line f(x)=x/( square root of 2x-1)
(lim_x→-2)((x−2)/(x+2))	Does Not Exist	Evaluate the Limit limit as x approaches -2 of (x-2)/(x+2)
d()/d(x)(∫_^)(cos(x)d(x))	cos(x)	Find the Derivative of the Integral integral of cos(x) with respect to x
(lim_x→−1)((x^3+1)/(x+1))	3	Evaluate the Limit
(∫_1^e)(ln(x)/x*d(x))	1/2	Evaluate the Integral
(∫_0^2π)(t^2sin(2t)d(t))	−2*π^2	Evaluate the Integral
(∫_^)((x^2+3x)cos(x)*d(x))	(x^2+3x−2)sin(x)+(2x+3)cos(x)+C	Evaluate the Integral
(∫_2^4)(3*d(x))	6	Evaluate the Integral
(∫_0^5)(√(,y+4)*d(y))	38/3	Evaluate the Integral
(∫_0^1)(arctan(x)*d(x))	π/4−ln(2)/2	Evaluate the Integral
(∫_−4^4)(√(,16−x^2)*d(x))	8*π	Evaluate the Integral
(∫_^)(x√(,2x+1)d(x))	1/10(2x+1)^(5/2)−1/6(2x+1)^(3/2)+C	Evaluate the Integral
(∫_^)(xcos(x)d(x))	x*sin(x)+cos(x)+C	Evaluate the Integral integral of x*cos(x) with respect to x
(∫_^)((e^u)/((6−e^u)^2)*d(u))	1/(6−e^u)+C	Evaluate the Integral
(∫_^)(x^5cos(x^3)d(x))	1/3x^3sin(x^3)+1/3*cos(x^3)+C	Evaluate the Integral
(∫_^)((17x+5)/(2x^2+7x−4)d(x))	3/2ln(abs(2x-1))+7*ln(abs(x+4))+C	Evaluate the Integral
(∫_^)(e^(3x−1)d(x))	(e^(3*x−1))/3+C	Evaluate the Integral integral of e^(3x-1) with respect to x
(∫_^)(√(,1−4x^2)d(x))	(x√(,1−4x^2))/2+arcsin(2x)/4+C	Evaluate the Integral
(∫_-1^1)(x*d(x))	0	Evaluate the Integral
(∫_^)(8x^7d(x))	x^8+C	Evaluate the Integral integral of 8x^7 with respect to x
(∫_^)(2xcos(x)*d(x))	2xsin(x)+2*cos(x)+C	Evaluate the Integral integral of 2xcos(x) with respect to x
(∫_^)(2sin(2x)*d(x))	−cos(2*x)+C	Evaluate the Integral integral of 2sin(2x) with respect to x
(∫_^)(3(2t+5)^3*d(t))	(3(2t+5)^4)/8+C	Evaluate the Integral integral of 3(2t+5)^3 with respect to t
(∫_0^π)((6+sin(x))*d(x))	6*π+2	Evaluate the Integral
(∫_^)(x√(,4−9x^2)d(x))	−1/27(4−9x^2)^(3/2)+C	Evaluate the Integral
(∫_^)(x/(1+x^4)*d(x))	1/2*arctan(x^2)+C	Evaluate the Integral integral of x/(1+x^4) with respect to x
(∫_^)(x/√(,x−1)*d(x))	2/3*(x−1)^(3/2)+2√(,x−1)+C	Evaluate the Integral
(∫_^)(x/√(,x+9)*d(x))	(2*(x−18)√(,x+9))/3+C	Evaluate the Integral
(∫_^)(cos(√(,x))*d(x))	2√(,x)sin(√(,x))+2cos(√(,x))+C	Evaluate the Integral
(∫_^)(√(,36−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_^)(e(5)^(5x)d(x))	e^(5*x)+C	Evaluate the Integral integral of e^(5x)(5) with respect to x
(∫_^)(−e^x*d(x))	−e^x+C	Evaluate the Integral integral of -e^x with respect to x
(∫_^)(xsec^2(x)d(x))	x*tan(x)-ln(abs(sec(x)))+C	Evaluate the Integral
(∫_^)(1/x*d(x))	ln(x)	Evaluate the Integral
(∫_^)(x^2cos(2x^3)*d(x))	sin(2*x^3)/6+C	Evaluate the Integral
(∫_^)(tan^4(x)*d(x))	tan^3(x)/3−tan(x)+x+C	Evaluate the Integral integral of tan(x)^4 with respect to x
(∫_1^2)(4x^3d(x))	15	Evaluate the Integral
(∫_^)(x^4e^(x^5)d(x))	(e^(x^5))/5+C	Evaluate the Integral integral of x^4e^(x^5) with respect to x
(∫_^)(12^x*d(x))	12^x/ln(12)+C	Evaluate the Integral integral of 12^x with respect to x
(∫_^)(sec^2(t)*d(t))	tan(t)+C	Evaluate the Integral integral of sec(t)^2 with respect to t
(∫_^)(4/(x^3)*d(x))	−2/(x^2)+C	Evaluate the Integral integral of 4/(x^3) with respect to x
(∫_^)((x^2)/√(,16−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_^)(((3+e^x)^2)/(e^x)*d(x))	−9e^(−x)+6x+e^x+C	Evaluate the Integral
(∫_1^2)(1/(1+x^4)*d(x))	see full solution →	Evaluate the Integral
(∫_^)((x^2)/(3−x^3)*d(x))	-1/3*ln(abs(3-x^3))+C	Evaluate the Integral
(∫_^)(sin(x)cos(x)d(x))	sin^2(x)/2+C	Evaluate the Integral
(∫_^)(x^5ln(x)d(x))	(x^6*ln(x))/6−(x^6)/36+C	Evaluate the Integral
(∫_^)(1/(4+x^2)*d(x))	1/2*arctan(x/2)+C	Evaluate the Integral integral of 1/(4+x^2) with respect to x
y=5	0	Find the 2nd Derivative y=5
ƒ(x)=√(,x^2+1)	1/((x^2+1)√(,x^2+1))	Find the 2nd Derivative f(x) = square root of x^2+1
d^2()/(d(x)^2)x(x−4)^3	12(x−4)(x−2)	Find the 2nd Derivative y=x(x-4)^3
d^2()/(d(x)^2)√(,x+12)	−1/(4*(x+12)^(3/2))	Find the 2nd Derivative y = square root of x+12
(∫_^)(12x^11−11/(x^11)d(x))	x^12+11/(10*x^10)+C	Evaluate the Integral
(∫_^)(b^2−5b+5d(b))	(b^3)/3−(5b^2)/2+5b+C	Evaluate the Integral integral of b^2-5b+5 with respect to b
(∫_^)(te^(−5t)*d(t))	−1/5te^(−5t)−1/25e^(−5*t)+C	Evaluate the Integral integral of te^(-5t) with respect to t
(∫_0^1)((x^2+3)e^(−x)d(x))	5−8/e	Evaluate the Integral
(∫_^)(((2+e^x)^2)/(e^x)*d(x))	−4e^(−x)+4x+e^x+C	Evaluate the Integral
(∫_^)((x+1)(3x−2)*d(x))	x^3+1/2x^2−2x+C	Evaluate the Integral
(∫_^)((x^2+1)^2*d(x))	(x^5)/5+(2*x^3)/3+x+C	Evaluate the Integral integral of (x^2+1)^2 with respect to x
(∫_^)((3x−2)^2d(x))	3x^3−6x^2+4*x+C	Evaluate the Integral integral of (3x-2)^2 with respect to x
d()/d(x)1/√(,x^17)	−17/(2*x^(19/2))	Find the Derivative - d/dx 1/( square root of x^17)
d()/d(x)(16^4√(,4x^4+4))	(262144*x^3)/√(,x^4+1)	Find the Derivative - d/dx y=16^4 square root of 4x^4+4
d()/d(y)xy^2	2xy	Find the Derivative - d/dy xy^2
d()/d(y)(1/(y^2)−5/(y^4))(y+7*y^3)	7+34/(y^2)+15/(y^4)	Find the Derivative - d/dy (1/(y^2)-5/(y^4))(y+7y^3)
d()/d(x)2x^(3/2)	3*x^(1/2)	Find the Derivative - d/dx 2x^(3/2)
d()/d(r)k(R^2−r^2)	−2kr	Find the Derivative - d/dr k(R^2-r^2)
(d(6)*sin(x))/d(x)	6*cos(x)	Find the Derivative - d/dx 6sin(x)
d()/d(x)*(√(,x)+1/√(3,x))^2	1+1/(3x^(5/6))−2/(3x^(5/3))	Find the Derivative - d/dx
(lim_x→8)(cos(1/x))	cos(1/8)	Evaluate the Limit limit as x approaches 8 of cos(1/x)
(lim_x→49)((√(,x)−7)/(x−49))	1/14	Evaluate the Limit
(lim_x→8)(√(,4x^2+x)−2x)	2√(,66)−16	Evaluate the Limit
(lim_x→∞)(√(,16x^2+x)−4x)	1/8	Evaluate the Limit
(lim_x→4)(ƒ(x))	ƒ(4)	Evaluate the Limit limit as x approaches 4 of f(x)
3x^4−16x^3+2016	Local Minimum: *(4,1760), Local Maxima: None	Find the Local Maxima and Minima 3x^4-16x^3+2016
ƒ(x)=e^(1−5*x^2)	Local Maximum: *(0,e), Local Minima: None	Find the Local Maxima and Minima f(x)=e^(1-5x^2)
3x^2−12x−8	Local Minimum: *(2,−20), Local Maxima: None	Find the Local Maxima and Minima 3x^2-12x-8
ƒ(x)=x^2−2*x−3	Local Minimum: *(1,−4), Local Maxima: None	Find the Local Maxima and Minima f(x)=x^2-2x-3
ƒ(x)=x+4/x	see full solution →	Find the Local Maxima and Minima f(x)=x+4/x
ƒ(x)=sin(x)+cos(x)	see full solution →	Find the Local Maxima and Minima f(x)=sin(x)+cos(x)
d()/d(x)xe^(−x)	e^(−x)*(1−x)	Find the Derivative - d/d@VAR f(x)=xe^(-x)
d(x^8)/d(x)	8*x^7	Find the Derivative - d/d@VAR f(x)=x^8
d()/d(x)1/(2*x^2)	−1/(x^3)	Find the Derivative - d/d@VAR f(x)=1/2x^2
d()/d(x)(3x^2−x)	6*x−1	Find the Derivative - d/d@VAR f(x)=3x^2-x
ƒ(x)=8/(x^2+1)	Local Maxima: *(0,8), Local Minima: None	Find the Local Maxima and Minima f(x)=8/(x^2+1)
(lim_x→5)((x^2−6*x+5)/(x−5))	4	Evaluate the Limit
(lim_x→8)(ln(x)/x)	ln(8)/8	Evaluate the Limit
(lim_x→−3)((x^2−9)/(x+3))	−6	Evaluate the Limit
(lim_x→5)((x^2−25)/(x−5))	10	Evaluate the Limit
(lim_x→0)(sin(4x)/sin(6x))	2/3	Evaluate the Limit
(lim_x→121)((√(,x)−11)/(x−121))	1/22	Evaluate the Limit
(lim_x→0)(e^x)	1	Evaluate the Limit limit as x approaches 0 of e^x
(lim_x→0)(sin(2x)/(3x))	2/3	Evaluate the Limit
(lim_x→4)((x−4)/(√(,x)−2))	4	Evaluate the Limit
d()/d(x)((x+9)*x)/(x+1)	(x^2+2*x+9)/((x+1)^2)	Find the Derivative - d/dx ((x+9)x)/(x+1)
(lim_x→1)((x−1)/(x^2−1))	1/2	Evaluate the Limit limit as x approaches 1 of (x-1)/(x^2-1)
(lim_x→2)(3x^2−5x+2)	4	Evaluate the Limit limit as x approaches 2 of 3x^2-5x+2
y=5−x^2,y=x−1	125/6	Find the Area Between the Curves y=5-x^2 , y=x-1
(lim_x→0)((1−cos(x))/x)	0	Evaluate the Limit ( limit as x approaches 0 of 1-cos(x))/x
(lim_x→0)((√(,x+9)−3)/x)	1/6	Evaluate the Limit
(lim_x→0)((√(,x+2)−√(,2))/x)	√(,2)/4	Evaluate the Limit
(lim_x→0)(x/x)	1	Evaluate the Limit
(lim_h→0)(((3+h)^2−9)/h)	6	Evaluate the Limit
(lim_h→0)(((x+h)^2−x^2)/h)	2*x	Evaluate the Limit
y=ln(√(,x))	ln(√(,x))=1/2*ln(x)	Graph natural log of square root of x
y=ln(1/x)	ln(1/x)=−ln(x)	Graph natural log of 1/x
ƒ(x)=1/ln(x)	1/ln(x)	Graph 1/( natural log of x)
v=√(,4^2+(−1)^2)	√(,17)	Solve for v v = square root of 4^2+(-1)^2
e^ln(x)	x	Simplify e^( natural log of x)
1/tan(x)	cot(x)	Simplify 1/(tan(x))
d(ln(x^2+y^2))/d(x)	(2x+2yd(y)/d(x))/(x^2+y^2)	Find the Derivative - d/dx natural log of x^2+y^2
d()/d(x)*(2^3⋅0)	0	Find the Derivative - d/dx 2^3*0
d()/d(x)1/(x^2+3)	−(2*x)/((x^2+3)^2)	Find the Derivative - d/dx 1/(x^2+3)
d()/d(x)1/(x−3)	−1/((x−3)^2)	Find the Derivative - d/dx 1/(x-3)
d()/d(x)1/(4√(,x)+x√(,x))	−(4+3x)/(2x√(,x)*(4+x)^2)	Find the Derivative - d/dx
d()/d(x)1/(4*x)	−1/(4*x^2)	Find the Derivative - d/dx 1/(4x)
d()/d(x)5ln(x)	5/x	Find the Derivative - d/dx 5 natural log of x
d()/d(x)1/(e^x)	−1/(e^x)	Find the Derivative - d/dx 1/(e^x)
d()/d(x)*(x−7)	1	Find the Derivative - d/dx x-7
d()/d(x)(x^2)/x	1	Find the Derivative - d/dx (x^2)/x
d()/d(x)(3x−9)/(2x+8)	21/(2*(x+4)^2)	Find the Derivative - d/dx (3x-9)/(2x+8)
d()/d(x)(x^2+1)/(x^2−1)	(−4*x)/((x^2−1)^2)	Find the Derivative - d/dx (x^2+1)/(x^2-1)
d()/d(x)((x+7)*x)/(x+1)	(x^2+2*x+7)/((x+1)^2)	Find the Derivative - d/dx ((x+7)x)/(x+1)
d()/d(x)(x^2)/(e^x)	(2*x−x^2)/(e^x)	Find the Derivative - d/dx (x^2)/(e^x)
d(e^9)/d(x)	0	Find the Derivative - d/dx e^9
d()/d(x)x(x^2+1)	3*x^2+1	Find the Derivative - d/dx y=x(x^2+1)
d()/d(x)((x+2)*x)/(x+1)	(x^2+2*x+2)/((x+1)^2)	Find the Derivative - d/dx y=((x+2)x)/(x+1)
d(e^8)/d(x)	0	Find the Derivative - d/dx e^8
d()/d(x)*(9/x−2/(x^3)+1/(x^4))	−9/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 9/x-2/(x^3)+1/(x^4)
(d(2)xe^x)/d(x)	2e^x(x+1)	Find the Derivative - d/dx 2xe^x
d()/d(x)[(x^3+x)(x^3−x)]	6x^5−2x	Find the Derivative - d/dx [(x^3+x)(x^3-x)]
d(e^(−6*x))/d(x)	−6e^(−6x)	Find the Derivative - d/dx e^(-6x)
d(3*x+4)/d(x)	6(3x+4)	Find the Derivative - d/dx (3x+4)^2
(d(9)*x^2)/d(x)	18*x	Find the Derivative - d/dx 9x^2
d()/d(x)(log_5)(xe^x)	(x+1)/(x*ln(5))	Find the Derivative - d/dx log base 5 of xe^x
d()/d(x)*x^(−5)	−5*x^(−6)	Find the Derivative - d/dx x^-5
d()/d(x)(4x−4)^2	32*x−32	Find the Derivative - d/dx (4x-4)^2
d()/d(x)(x^2−6x+2)/(2x)	1/2−1/(x^2)	Find the Derivative - d/dx (x^2-6x+2)/(2x)
(d(−)2x^3)/d(x)	−6*x^2	Find the Derivative - d/dx -2x^3
d()/d(x)((x^4)/4+1/(8x^2))	x^3−1/(4*x^3)	Find the Derivative - d/dx (x^4)/4+1/(8x^2)
d()/d(x)x/(x^2+3)	(3−x^2)/((x^2+3)^2)	Find the Derivative - d/dx x/(x^2+3)
d()/d(x)*y=0	0	Find the Derivative - d/dx y=0
d()/d(x)*x^(1/4)	1/4*x^(−3/4)	Find the Derivative - d/dx x^(1/4)
d()/d(x)(5√(,x))/8	5/(16√(,x))	Find the Derivative - d/dx (5 square root of x)/8
d(tan(4*x))/d(x)	4sec^2(4x)	Find the Derivative - d/dx tan(4x)
d()/d(x)ln(x)/x	(1−ln(x))/(x^2)	Find the Derivative - d/dx ( natural log of x)/x
d()/d(x)((x+4)*x)/(x+1)	(x^2+2*x+4)/((x+1)^2)	Find the Derivative - d/dx y=((x+4)x)/(x+1)
d()/d(x)(2x^2−x−3)	4*x−1	Find the Derivative - d/dx 2x^2-x-3
d()/d(x)x^2(1−6*x)	2x−18x^2	Find the Derivative - d/dx x^2(1-6x)
d()/d(x)1/√(,x^13)	−13/(2*x^(15/2))	Find the Derivative - d/dx 1/( square root of x^13)
d()/d(x)(2x−1)	2	Find the Derivative - d/dx 2x-1
d()/d(x)3x^2*y	6xy+3*x^2d(y)/d(x)	Find the Derivative - d/dx 3x^2y
d()/d(x)(3*x)/(x^2+1)	(3−3*x^2)/((x^2+1)^2)	Find the Derivative - d/dx (3x)/(x^2+1)
d()/d(x)4/(3*x^2)	−8/(3*x^3)	Find the Derivative - d/dx 4/(3x^2)
d()/d(x)*(7+sin(x))	cos(x)	Find the Derivative - d/dx y=7+sin(x)
d(sin(8*x))/d(x)	8cos(8x)	Find the Derivative - d/dx sin(8x)
d(x^(3/4))/d(x)	3/4*x^(−1/4)	Find the Derivative - d/dx x^(3/4)
d()/d(x)x(x^2−1/x)	3*x^2	Find the Derivative - d/dx x(x^2-1/x)
d()/d(x)√(,7−x)	−1/(2√(,7−x))	Find the Derivative - d/d@VAR g(x) = square root of 7-x
d()/d(x)*(x^2+3)	2*x	Find the Derivative - d/d@VAR f(x)=x^2+3
d()/d(x)(x^3+x+4)/(2*x)	x−2/(x^2)	Find the Derivative - d/d@VAR f(x)=(x^3+x+4)/(2x)
d()/d(x)1/(x^4)	−4/(x^5)	Find the Derivative - d/d@VAR f(x)=1/(x^4)
(d(sec(x))*tan(x))/d(x)	sec^3(x)+sec(x)*tan^2(x)	Find the Derivative - d/dx sec(x)tan(x)
d(sin(2*t))/d(t)	2cos(2t)	Find the Derivative - d/dt sin(2t)
d()/d(t)(e^(−t))/(1+t^2)	−(e^(−t)*(t+1)^2)/((1+t^2)^2)	Find the Derivative - d/dt (e^(-t))/(1+t^2)
d()/d(r)(312pr−6p^2*r^2)	312p−12p^2*r	Find the Derivative - d/dr 312pr-6p^2r^2
d()/d(m)(mx+b)	x	Find the Derivative - d/dm mx+b
√(,t)/(t^2)	1/(t^(3/2))	Simplify ( square root of t)/(t^2)
d(V)/d(r)* where V=4/3π*r^3	4πr^2	Find dV/dr V=4/3*(pr^3)
(∫_^)(√(3,x)*d(x))	(3*x^(4/3))/4+C	Find the Integral cube root of x
(∫_^)(√(4,x)*d(x))	4/5*x^(5/4)+C	Find the Integral fourth root of x
(∫_^)(1/(e^x)*d(x))	−e^(−x)+C	Find the Integral 1/(e^x)
d(sin(sin(sin(x))))/d(x)	cos(sin(sin(x)))⋅cos(sin(x))⋅cos(x)	Find the Derivative - d/dx y=sin(sin(sin(x)))
d()/d(y)1/(y^2)	−2/(y^3)	Find the Derivative - d/dy 1/(y^2)
d(e^(2*y))/d(y)	2e^(2y)	Find the Derivative - d/dy e^(2y)
d()/d(y)(1/(y^2)−3/(y^4))(y+9*y^3)	9+26/(y^2)+9/(y^4)	Find the Derivative - d/dy (1/(y^2)-3/(y^4))(y+9y^3)
d()/d(x)*2^2⋅0	0	Find the Derivative - d/dx 2^2*0
d(ln(√(3,x)))/d(x)	1/(3*x)	Find the Derivative - d/dx natural log of cube root of x
d()/d(x)x^2(1−4*x)	2x−12x^2	Find the Derivative - d/dx x^2(1-4x)
d()/d(x)sin(x)/(1+cos(x))	1/(1+cos(x))	Find the Derivative - d/dx (sin(x))/(1+cos(x))
d(csc(x))/d(x)	−csc(x)*cot(x)	Find the Derivative - d/dx y=csc(x)
d()/d(x)*(x/4−4/x)	1/4+4/(x^2)	Find the Derivative - d/dx y=x/4-4/x
d()/d(x)x√(,3x+1)	(9x+2)/(2√(,3x+1))	Find the Derivative - d/dx x square root of 3x+1
d()/d(x)*e^sin(x)	e^sin(x)*cos(x)	Find the Derivative - d/dx y=e^(sin(x))
d()/d(x)√(,1−x^2)	−x/√(,1−x^2)	Find the Derivative - d/dx y = square root of 1-x^2
d()/d(x)*(5−x^2)	−2*x	Find the Derivative - d/dx 5-x^2
d()/d(x)x/√(,x^2+1)	1/((x^2+1)^(3/2))	Find the Derivative - d/dx y=x/( square root of x^2+1)
(d(4)*tan(x))/d(x)	4*sec^2(x)	Find the Derivative - d/dx 4tan(x)
(d(3)*sec(x))/d(x)	3sec(x)tan(x)	Find the Derivative - d/dx 3sec(x)
d()/d(x)*x^(−1/2)	−1/2*x^(−3/2)	Find the Derivative - d/dx x^(-1/2)
d()/d(x)x^7e^x	x^6e^x(x+7)	Find the Derivative - d/dx x^7e^x
d()/d(x)*11^x	11^x*ln(11)	Find the Derivative - d/dx y=11^x
d()/d(x)2/(x^2)	−4/(x^3)	Find the Derivative - d/dx y=2/(x^2)
d()/d(x)(x+1)^2(x^2+1)^(−3)	(2(x+1)(−2x^2−3x+1))/((x^2+1)^4)	Find the Derivative - d/dx y=(x+1)^2(x^2+1)^-3
d()/d(x)*(√(,x)+3/√(,x))	1/(2√(,x))−3/(2*x√(,x))	Find the Derivative - d/dx square root of x+3/( square root of x)
d(ln(e^(x^2)))/d(x)	2*x	Find the Derivative - d/dx natural log of e^(x^2)
d(ln(e^x+x*e^x))/d(x)	(x+2)/(x+1)	Find the Derivative - d/dx natural log of e^x+xe^x
d(ln((x+1)/(x−1)))/d(x)	(−2)/(x^2−1)	Find the Derivative - d/dx natural log of (x+1)/(x-1)
d(cos(2*x))/d(x)	−2sin(2x)	Find the Derivative - d/dx f(x)=cos(2x)
(d(x)*sin(x))/d(x)	x*cos(x)+sin(x)	Find the Derivative - d/dx f(x)=xsin(x)
x^2−4xy+y^2=4	(2y−x)/(y−2x)	Find dy/dx x^2-4xy+y^2=4
d()/d(x)(xcos(x)+sin(x))	2cos(x)−xsin(x)	Find the Derivative - d/dx xcos(x)+sin(x)
d()/d(x)*(x^3−1)	3*x^2	Find the Derivative - d/dx x^3-1
d()/d(x)(x+3)(x^2−3)	3x^2+6x−3	Find the Derivative - d/dx (x+3)(x^2-3)
d()/d(x)ln((e^(x^2)(3x−2)^7)/(7x^9))	2x+21/(3x−2)−9/x	Find the Derivative - d/dx natural log of (e^(x^2)(3x-2)^7)/(7x^9)
d()/d(x)5/√(,x)	−5/(2*x√(,x))	Find the Derivative - d/dx 5/( square root of x)
d()/d(x)(7√(,x))/8	7/(16√(,x))	Find the Derivative - d/dx (7 square root of x)/8
d(sin(7*x))/d(x)	7cos(7x)	Find the Derivative - d/dx sin(7x)
d()/d(x)(−x+8)/(x+1)	−9/((x+1)^2)	Find the Derivative - d/dx -x+8/x+1
d()/d(x)(x^3−3*x^2+4)/(x^2)	1−8/(x^3)	Find the Derivative - d/dx (x^3-3x^2+4)/(x^2)
(d(sin(x))*tan(x))/d(x)	sin(x)*sec^2(x)+sin(x)	Find the Derivative - d/dx sin(x)tan(x)
d()/d(x)*(sin(x)−cos(x))	cos(x)+sin(x)	Find the Derivative - d/dx sin(x)-cos(x)
d(ln(x+2))/d(x)	1/(x+2)	Find the Derivative - d/dx natural log of x+2
d(e^∞)/d(x)	0	Find the Derivative - d/dx e^infinity
d()/d(x)(3x^2−2*x)	6*x−2	Find the Derivative - d/dx 3x^2-2x
d((log_)(2*x))/d(x)	1/(x*ln(10))	Find the Derivative - d/dx log of 2x
d()/d(x)(x^2+3x)	2*x+3	Find the Derivative - d/dx x^2+3x
d()/d(x)(x^2)/(x^2+1)	(2*x)/((x^2+1)^2)	Find the Derivative - d/dx f(x)=(x^2)/(x^2+1)
(d(5)*tan(x))/d(x)	5*sec^2(x)	Find the Derivative - d/dx 5tan(x)
d()/d(x)(3x+5)	3	Find the Derivative - d/dx 3x+5
d(arctan(2*x))/d(x)	2/(1+4*x^2)	Find the Derivative - d/dx arctan(2x)
d()/d(x)*(e^x+x^e)	e^x+e*x^(e−1)	Find the Derivative - d/dx e^x+x^e
d(cos(tan(x)))/d(x)	−sec^2(x)*sin(tan(x))	Find the Derivative - d/dx cos(tan(x))
d(cos(7*x))/d(x)	−7sin(7x)	Find the Derivative - d/dx cos(7x)
d()/d(x)9/(8√(4,x^3))	−27/(32√(4,x^7))	Find the Derivative - d/dx 9/(8 fourth root of x^3)
d()/d(x)*(1+sin(x))	cos(x)	Find the Derivative - d/dx 1+sin(x)
(d(csc(x))*cot(x))/d(x)	−csc^3(x)−csc(x)*cot^2(x)	Find the Derivative - d/dx csc(x)cot(x)
d(x^x)/d(x)	x^x*(ln(x)+1)	Find the Derivative - d/dx f(x)=x^x
d(x^5)/d(x)	5*x^4	Find the Derivative - d/dx f(x)=x^5
(∫_^)(te^td(t))	t*e^t−e^t+C	Evaluate the Integral integral of te^t with respect to t
d(x^(5/2))/d(x)	5/2*x^(3/2)	Find the Derivative - d/dx f(x)=x^(5/2)
d()/d(x)*(x^2+1)	2*x	Find the Derivative - d/dx f(x)=x^2+1
d()/d(x)*3^x	3^x*ln(3)	Find the Derivative - d/d@VAR f(x)=3^x
d()/d(x)2/x	−2/(x^2)	Find the Derivative - d/d@VAR F(x)=2/x
d(x^6)/d(x)	6*x^5	Find the Derivative - d/d@VAR f(x)=x^6
(∫_^)(2x^2d(x))	(2*x^3)/3+C	Find the Integral 2x^2
(∫_^)(sin^3(x)*d(x))	cos^3(x)/3−cos(x)+C	Find the Integral sin(x)^3
x^3+y^3=18xy	(6y−x^2)/(y^2−6x)	Find dy/dx x^3+y^3=18xy
x^2+6y^2+6y=20	−x/(6*y+3)	Find dy/dx x^2+6y^2+6y=20
sin(x^2*y^2)=x	(1−2xy^2cos(x^2y^2))/(2x^2ycos(x^2y^2))	Find dy/dx sin(x^2y^2)=x
2xy+y^2=x+y	(1−2y)/(2x+2*y−1)	Find dy/dx 2xy+y^2=x+y
(∫_^)(cot^2(x)*d(x))	−cot(x)−x+C	Evaluate the Integral integral of cot(x)^2 with respect to x
e^(x/y)=x−y	(y^2−ye^(x/y))/(y^2−xe^(x/y))	Find dy/dx e^(x/y)=x-y
d()/d(x)2/(x^2)	−4/(x^3)	Find the Derivative - d/d@VAR f(x)=2/(x^2)
d(y)/d(x)* for *y=x^x	x^x*(1+ln(x))	Find dy/dx y=x^x
d(e^ln(x))/d(x)	1	Find the Derivative - d/dx e^( natural log of x)
(d(4)*ln(x))/d(x)	4/x	Find the Derivative - d/dx 4 natural log of x
ysin(x^2)=xsin(y^2)	(sin(y^2)−2xycos(x^2))/(sin(x^2)−2xycos(y^2))	Find dy/dx ysin(x^2)=xsin(y^2)
d()/d(x)sec(x)tan(x)	sec(x)*(sec^2(x)+tan^2(x))	Find the Derivative - d/dz y=sec(x)tan(x)
d()/d(x)(2x^2+3*x−2)	4*x+3	Find the Derivative - d/dx 2x^2+3x-2
d(tan(x))/d(x)	4tan(x)sec(x)	Find the Derivative - d/dx tan(x)^4
d()/d(x)4sec^2(x)	8sec^2(x)tan(x)	Find the Derivative - d/dx 4sec(x)^2
d(e^(−x/2))/d(x)	−1/2*e^(−x/2)	Find the Derivative - d/dx e^(-x/2)
d(cos(x))/d(x)	−5cos(x)sin(x)	Find the Derivative - d/dx cos(x)^5
d()/d(x)(3−x*e^x)/(x+e^x)	(−(x^2e^x+e^(2x)+3*e^x+3))/((x+e^x)^2)	Find the Derivative - d/dx (3-xe^x)/(x+e^x)
d()/d(t)4t	4	Find the Derivative - d/dt 4t
d()/d(t)−1/((3+t)^2)	2/((3+t)^3)	Find the Derivative - d/dt -1/((3+t)^2)
(d(8)*sin(x))/d(x)	8*cos(x)	Find the Derivative - d/dx 8sin(x)
(d(−)2cos(x))/d(x)	2*sin(x)	Find the Derivative - d/dx -2cos(x)
d^2(x^3)/(d(x)^2)	6*x	Find the 2nd Derivative x^3
(lim_x→8)(arctan(e^x))	arctan(e^8)	Evaluate Using L'Hospital's Rule limit as x approaches 8 of arctan(e^x)
(lim_x→0)(e^x+x)	e^2	Evaluate Using L'Hospital's Rule limit as x approaches 0 of (e^x+x)^(1/x)
(∫_^)((e^x+e^(−x))/(e^x−e^(−x))*d(x))	ln(abs(e^x-e^(-x)))+C	Evaluate the Integral
(∫_^)(((ln(x))^6)/x*d(x))	((ln(x))^7)/7+C	Evaluate the Integral
(∫_^)(x/2*d(x))	(x^2)/4+C	Evaluate the Integral integral of x/2 with respect to x
(∫_0^1)(2xe^x*d(x))	2	Evaluate the Integral
(∫_^)(1/√(,x^2+100)*d(x))	ln(abs(x+√(2,x^2+100)))+C	Evaluate the Integral
(∫_1^e)(ln(x)*d(x))	1	Evaluate the Integral
(∫_^)(3e^xd(x))	3*e^x+C	Evaluate the Integral integral of 3e^x with respect to x
(∫_^)(xln(3+x)d(x))	(x^2−9)/2ln(3+x)−(x^2)/4+(3x)/2+C	Evaluate the Integral
d^2(cos(x^2))/(d(x)^2)	−4x^2cos(x^2)−2*sin(x^2)	Find the 2nd Derivative cos(x^2)
ƒ(x)=√(,x^2+11)	11/((x^2+11)√(,x^2+11))	Find the 2nd Derivative f(x) = square root of x^2+11
ƒ(x)=√(,x^2+27)	27/((x^2+27)√(,x^2+27))	Find the 2nd Derivative f(x) = square root of x^2+27
y=−2	0	Find the 2nd Derivative y=-2
d^2()/(d(x)^2)√(,x+6)	−1/(4*(x+6)^(3/2))	Find the 2nd Derivative y = square root of x+6
d^2()/(d(x)^2)x(x−4)^3	12(x−4)(x−2)	Find the 2nd Derivative x(x-4)^3
d^2()/(d(x)^2)e^(7x^2+3)	14e^(7x^2+3)(14x^2+1)	Find the 2nd Derivative f(x)=e^(7x^2+3)
(lim_x→−5)((x^2−25)/(x+5))	−10	Evaluate the Limit
(∫_^)(1/(4−x^2)*d(x))	1/4*ln(abs((x+2)/(x-2)))+C	Evaluate the Integral
(∫_^)(1/ln(x)*d(x))	li(x)+C	Evaluate the Integral
(∫_^)(xcos(4x)*d(x))	(xsin(4x))/4+cos(4*x)/16+C	Evaluate the Integral integral of xcos(4x) with respect to x
(∫_^)(1/(xln(x))d(x))	−1/ln(x)+C	Evaluate the Integral
(∫_^)(1/(1+√(,x))*d(x))	2√(,x)−2*ln(1+√(,x))+C	Evaluate the Integral
(∫_^)(1/(√(3,x)+√(4,x))*d(x))	see full solution →	Evaluate the Integral
(∫_0^1)((x^2+2)e^(−x)d(x))	4−7/e	Evaluate the Integral
(∫_^)(1/√(,2x)d(x))	√(,2*x)+C	Evaluate the Integral
(∫_^)(arctan(2t)d(t))	tarctan(2t)−1/4ln(1+4t^2)+C	Evaluate the Integral integral of arctan(2t) with respect to t
(∫_^)((xe^(2x))/((2x+1)^2)d(x))	(e^(2x))/(4(2*x+1))+C	Evaluate the Integral
(∫_^)((x^3)/3*d(x))	(x^4)/12+C	Evaluate the Integral integral of (x^3)/3 with respect to x
(∫_^)((x^3−7)/x*d(x))	1/3x^3-7ln(abs(x))+C	Evaluate the Integral
(∫_^)(cos(8x)d(x))	sin(8*x)/8+C	Evaluate the Integral integral of cos(8x) with respect to x
(∫_^)((6+x^2)/x*d(x))	6ln(abs(x))+1/2x^2+C	Evaluate the Integral
(∫_^)(z/(e^z)*d(z))	−(z+1)/(e^z)+C	Evaluate the Integral integral of z/(e^z) with respect to z
(∫_^)((2x^2+7x−3)/(x−2)*d(x))	x^2+11x+19ln(abs(x-2))+C	Evaluate the Integrral
22(∫_0^1)(x^3√(,1−x^2)d(x))	44/15	Evaluate the Integral
(∫_^)(xsin(4x)*d(x))	−x/4cos(4x)+1/16sin(4x)+C	Evaluate the Integral integral of xsin(4x) with respect to x
(∫_^)((4−5x)^6d(x))	−((4−5*x)^7)/35+C	Evaluate the Integral integral of (4-5x)^6 with respect to x
(∫_0^5)(√(,x^2+25)*d(x))	(25√(,2))/2+25/2*ln(1+√(,2))	Evaluate the Integral
(∫_0^3)(√(,5)*d(x))	3√(,5)	Evaluate the Integral
(∫_^)(sin(x)/(1+cos(x))*d(x))	-ln(abs(1+cos(x)))+C	Evaluate the Integral
(∫_^)(√(,1−x)*d(x))	−2/3*(1−x)^(3/2)+C	Evaluate the Integral
(∫_^)(tan^3(x)sec(x)d(x))	sec^3(x)/3−sec(x)+C	Evaluate the Integral
(∫_^)(cot^3(x)*d(x))	-1/2*cot^2(x)-ln(abs(sin(x)))+C	Evaluate the Integral
(∫_0^1)((x^2+5)e^(−x)d(x))	7−10/e	Evaluate the Integral
(∫_^)(e^(2x)(1+e^(2x))^3d(x))	((1+e^(2*x))^4)/8+C	Evaluate the Integral
(∫_^)(e^(−x/2)*d(x))	−2*e^(−x/2)+C	Evaluate the Integral integral of e^(-x/2) with respect to x
(∫_^)(ln(x)/(x^4)*d(x))	−(3ln(x)+1)/(9x^3)+C	Evaluate the Integral
(∫_^)(ln(5x)/xd(x))	((ln(5*x))^2)/2+C	Evaluate the Integral
(∫_^)(x^(4/3)*d(x))	(3*x^(7/3))/7+C	Evaluate the Integral integral of x^(4/3) with respect to x
(∫_^)(x/√(,x−3)*d(x))	(2*(x+6)√(,x−3))/3+C	Evaluate the Integral
(∫_^)(x^2√(,x+1)*d(x))	see full solution →	Evaluate the Integral
(∫_^)(x^2sin(x)d(x))	−x^2cos(x)+2xsin(x)+2cos(x)+C	Evaluate the Integral integral of x^2*sin(x) with respect to x
(∫_-1^2)((x-8abs(x))d(x))	-37/2	Evaluate the Integral
d()/d(x)1/(x^3)	−3/(x^4)	Find the Derivative - d/d@VAR f(x)=1/(x^3)
(∫_^)(√(,x−1)*d(x))	2/3*(x−1)^(3/2)+C	Evaluate the Integral
(∫_^)(x√(,4−x)*d(x))	2/5(4−x)^(5/2)−8/3(4−x)^(3/2)+C	Evaluate the Integral
(∫_^)(1/(1+cos(x))*d(x))	tan(x/2)+C	Evaluate the Integral
(∫_^)((x+4)/√(,x)*d(x))	2/3x^(3/2)+8x^(1/2)+C	Evaluate the Integral
(∫_^)(−32*d(t))	−32*t+C	Evaluate the Integral integral of -32 with respect to t
(∫_^)(3x^5d(x))	1/2*x^6+C	Evaluate the Integral integral of 3x^5 with respect to x
(∫_^)((x^2+10x)cos(x)*d(x))	(x^2+10x−2)sin(x)+(2x+10)cos(x)+C	Evaluate the Integral
(∫_^)(e^t*d(t))	e^t+C	Evaluate the Integral integral of e^t with respect to t
(∫_^)(4(4x+3)^4*d(x))	((4*x+3)^5)/5+C	Evaluate the Integral integral of 4(4x+3)^4 with respect to x
(d(2)sin(2x))/d(x)	4cos(2x)	Find the Derivative - d/dx 2sin(2x)
(∫_^)(x^3sin(x)d(x))	−x^3cos(x)+3x^2sin(x)+6xcos(x)−6sin(x)+C	Evaluate the Integral integral of x^3sin(x) with respect to x
(∫_0^π)(cos(x)*d(x))	0	Evaluate the Integral
(∫_^)(3x(x^2−3)^7*d(x))	3/16*(x^2−3)^8+C	Evaluate the Integral
(∫_^)(te^(−6t)*d(t))	−1/6te^(−6t)−1/36e^(−6*t)+C	Evaluate the Integral integral of te^(-6t) with respect to t
(∫_^)(sec(2x)tan(2x)d(x))	1/2sec(2x)+C	Evaluate the Integral
(∫_^)(xcos(2x)*d(x))	1/2xsin(2x)+1/4cos(2*x)+C	Evaluate the Integral integral of xcos(2x) with respect to x
(∫_0^1)(e^x*d(x))	e−1	Evaluate the Integral
(∫_^)(x√(,x−7)*d(x))	2/5(x−7)^(5/2)+14/3(x−7)^(3/2)+C	Evaluate the Integral
(∫_0^1)(x^9(1+x^10)^9d(x))	10.23	Evaluate the Integral
(∫_^)(ln(5x−4)d(x))	(x−4/5)ln(5x−4)−x+C	Evaluate the Integral
(∫_^)((x^3)/√(,x^2+4)*d(x))	((x^2−8)√(,x^2+4))/3+C	Evaluate the Integral
(∫_0^2)(e^x*d(x))	e^2−1	Evaluate the Integral
(∫_^)(cos(x/5)*d(x))	5*sin(x/5)+C	Evaluate the Integral integral of cos(x/5) with respect to x
(∫_0^1)(b√(,1−b^2)*d(b))	1/3	Evaluate the Integral
(∫_0^1)(xe^(x^2)d(x))	(e−1)/2	Evaluate the Integral
(∫_^)(x√(,1−x)*d(x))	2/5(1−x)^(5/2)−2/3(1−x)^(3/2)+C	Evaluate the Integral
(∫_0^5)(x*d(x))	25/2	Evaluate the Integral
(∫_0^3)(3xd(x))	27/2	Evaluate the Integral
(∫_^)(xe^(6x)*d(x))	1/6xe^(6x)−1/36e^(6*x)+C	Evaluate the Integral integral of xe^(6x) with respect to x
(∫_1^5)(x/√(,2x−1)d(x))	16/3	Evaluate the Integral
(∫_^)(5/x*d(x))	5*ln(x)	Evaluate the Integral
(∫_0^4)(x^2*d(x))	64/3	Evaluate the Integral
(∫_0^3)(2x-3d(x))	0	Evaluate the Integral
(∫_0^3)(x-1*d(x))	3/2	Evaluate the Integral
(∫_0^2)(6x^2d(x))	16	Evaluate the Integral
(∫_0^2)(x(x−3)d(x))	−10/3	Evaluate the Integral
(∫_7^8)(x√(,x−7)*d(x))	76/15	Evaluate the Integral
(∫_1^16)((x−5)/√(,x)*d(x))	12	Evaluate the Integral
(∫_^)((a+bx^2)/√(,3ax+bx^3)*d(x))	(2√(,3ax+b*x^3))/3+C	Evaluate the Integral
(∫_1^5)(x^2*d(x))	124/3	Evaluate the Integral
10.2/√(,36.0+(10.2)^2)⋅440	see full solution →	Evaluate
d()/d(x)(∫_^)(12x(x^2+3)^5d(x))	12x(x^2+3)^5	Find the Derivative of the Integral
d()/d(x)(∫_^)(√(3,x^2)d(x))	√(3,x^2)	Find the Derivative of the Integral
(∫_^)(1/(x^2−1)*d(x))	1/2*ln(abs((x-1)/(x+1)))+C	Evaluate the Integral
(lim_x→∞)(√(,4x^2+x)−2x)	1/4	Evaluate the Limit
(lim_x→0)((3x−sin(3x))/(3x−tan(3x)))	−1/2	Evaluate the Limit
(∫_^)(u^2√(,u^3+2)*d(u))	2/9*(u^3+2)^(3/2)+C	Evaluate the Integral
(∫_0^π)(xsin(x)d(x))	π	Evaluate the Integral
ƒ(x)=x+1/x	−1,1	Find the Critical Points f(x)=x+1/x
x^2+y^2=−2*x	1, y = -1	Find the Horizontal Tangent Line x^2+y^2=-2x
x^2+y^2=−12*x	6, y = -6	Find the Horizontal Tangent Line x^2+y^2=-12x
x^2+y^2=20*x	10, y = -10	Find the Horizontal Tangent Line x^2+y^2=20x
x^2+y^2=6*x	3, y = -3	Find the Horizontal Tangent Line x^2+y^2=6x
y=x^3−3*x^2+1	1, y = -3	Find the Horizontal Tangent Line y=x^3-3x^2+1
x^3+3x^2y+y^3=8	0* when x=0 or x=−2y	Find Where dy/dx is Equal to Zero x^3+3x^2y+y^3=8
√(,5^2+(−4)^2)	√(,41)	Evaluate square root of 5^2+(-4)^2
tan(3)	tan(3)≈−0.1425	Evaluate tan(3)
ƒ(x)=(4*x)/(x^2+1)	−1,1	Find the Critical Points f(x)=(4x)/(x^2+1)
ƒ(x)=x^6−6*x^5	0, 5	Find the Critical Points f(x)=x^6-6x^5
d()/d(x)√(,10)/(x^7)	−(7√(,10))/(x^8)	Find the Derivative - d/dx ( square root of 10)/(x^7)
d()/d(x)*(x^3+x)	3*x^2+1	Find the Derivative - d/dx x^3+x
(∫_^)(x^4sin(x^5)d(x))	−cos(x^5)/5+C	Evaluate the Integral
(∫_^)((e^x)/(1+e^x)*d(x))	ln(1+e^x)+C	Evaluate the Integral
d()/d(x)(xln(x)−x)	ln(x)	Find the Derivative - d/dx x natural log of x-x
(d(8)*x^3)/d(x)	24*x^2	Find the Derivative - d/dx 8x^3
e^(x^2+y)=x+y	(1−2xe^(x^2+y))/(e^(x^2+y)−1)	Find dy/dx e^(x^2+y)=x+y
x^2*y^2=36	−y/x	Find dy/dx x^2y^2=36
x^2+y^2=36	−x/y	Find dy/dx x^2+y^2=36
(∫_^)(cos(x)*d(x))	sin(x)−(2*sin(x))/3+sin(x)/5+C	Evaluate the Integral integral of cos(x)^5 with respect to x
x^3+y^3=6xy	(2y−x^2)/(y^2−2x)	Find dy/dx x^3+y^3=6xy
2x^2−3y^2=5	(2x)/(3y)	Find dy/dx 2x^2-3y^2=5
(lim_x→∞)(ƒ(x))	L	Evaluate the Limit limit as x approaches infinity of f(x)
d(√(,x))/d(x)	((√(,x))^x*(ln(x)+1))/2	Find the Derivative - d/dx ( square root of x)^x
d(v)/d(p)* where v=4/3π*r^3	0	Find dv/dp v=4/3*(pr^3)
2√(,x)+√(,y)=3	−(2√(,y))/√(,x)	Find dy/dx 2 square root of x+ square root of y=3
(d(2)cos(2x))/d(x)	−4sin(2x)	Find the Derivative - d/dx 2cos(2x)
(lim_x→5)((x^2−6*x+5)/(x−5))	4	Evaluate the Limit
(∫_^)(e^t*d(t))	e^t+C	Find the Integral e^t
(∫_^)((x−1)(x^2−2x+5)^5*d(x))	((x^2−2*x+5)^6)/12+C	Find the Integral (x-1)(x^2-2x+5)^5
d()/d(x)*(x^2+2)	2*x	Find the Derivative - d/d@VAR f(x)=x^2+2
d()/d(x)2x^3	6*x^2	Find the Derivative - d/d@VAR f(x)=2x^3
d(e^(3*x))/d(x)	3e^(3x)	Find the Derivative - d/d@VAR f(x)=e^(3x)
d()/d(x)7x^2	14*x	Find the Derivative - d/d@VAR f(x)=7x^2
d()/d(x)(2x^2−9*x+10)	4*x−9	Find the Derivative - d/d@VAR f(x)=2x^2-9x+10
d()/d(r)4/3πr^3	4πr^2	Find the Derivative - d/d@VAR f(r)=4/3pir^3
d()/d(x)(2x^2−7*x+5)	4*x−7	Find the Derivative - d/d@VAR f(x)=2x^2-7x+5
d()/d(x)*(x^2+10)^6	12x(x^2+10)^5	Find the Derivative - d/d@VAR f(x)=(x^2+10)^6
d(e^tan(x))/d(x)	e^tan(x)*sec^2(x)	Find the Derivative - d/dx e^(tan(x))
d(x^10)/d(x)	10*x^9	Find the Derivative - d/dx f(x)=x^10
(∑_n=0^4)((n^2)/2)	15	Evaluate the Summation sum from n=0 to 4 of (n^2)/2
√(,x−5)/(x−25)	√(,x−5)/(x−25)	Simplify ( square root of x-5)/(x-25)
(lim_x→49)((7−√(,x))/(49*x−x^2))	1/686	Evaluate the Limit
x^4−6*x^2+5	(1,0),(−1,0)	Find the Inflection Points x^4-6x^2+5
d(e^(3*x))/d(x)	3e^(3x)	Find the Derivative - d/dx f(x)=e^(3x)
d(e^(−x^2))/d(x)	−2xe^(−x^2)	Find the Derivative - d/dx f(x)=e^(-x^2)
d()/d(x)e^xln(x)	e^x*(1/x+ln(x))	Find the Derivative - d/dx f(x)=e^x natural log of x
d(5^x)/d(x)	5^x*ln(5)	Find the Derivative - d/dx f(x)=5^x
d()/d(x)*x^8	8*x^7	Find the Derivative - d/dx f(x)=x^8
d(cot(3*x))/d(x)	−3csc^2(3x)	Find the Derivative - d/dx cot(3x)
d(cos(x^3))/d(x)	−3x^2sin(x^3)	Find the Derivative - d/dx cos(x^3)
d(9^x)/d(x)	9^x*ln(9)	Find the Derivative - d/dx 9^x
d(x-4)/d(x)	1	Find the Derivative - d/dx x-4
d()/d(x)4/(x^3)	−12/(x^4)	Find the Derivative - d/dx 4/(x^3)
d(arcsin(2*x))/d(x)	2/√(,1−4*x^2)	Find the Derivative - d/dx arcsin(2x)
d()/d(x)1/(8*x^2)	−1/(4*x^3)	Find the Derivative - d/dx 1/(8x^2)
(d(6)e^xcos(x))/d(x)	6e^x(cos(x)−sin(x))	Find the Derivative - d/dx 6e^xcos(x)