Calculus — Full Problem Index (2/3)

Problem	Final Answer	Solution
d()/d(x)(2x^2−3x+1)/x	2−1/(x^2)	Find the Derivative - d/dx f(x)=(2x^2-3x+1)/x
d((log_)(x^2))/d(x)	2/(x*ln(10))	Find the Derivative - d/dx log of x^2
d((log_)(6*x))/d(x)	1/(x*ln(10))	Find the Derivative - d/dx log of 6x
d()/d(x)(−2)/(x^2)	4/(x^3)	Find the Derivative - d/dx -2/(x^2)
d(sec(3*x))/d(x)	3sec(3x)tan(3x)	Find the Derivative - d/dx sec(3x)
d()/d(x)9e^x√(,x)	(9e^x)/(2√(,x))+9e^x√(,x)	Find the Derivative - d/dx 9e^x square root of x
d(ln(3*x))/d(x)	1/x	Find the Derivative - d/dx f(x) = natural log of 3x
(d(sin(x))*cos(x))/d(x)	cos(2*x)	Find the Derivative - d/dx f(x)=sin(x)cos(x)
d()/d(x)*x√(,x)	(3√(,x))/2	Find the Derivative - d/dx f(x)=x square root of x
d()/d(x)*(x+1)	1	Find the Derivative - d/dx f(x)=x+1
d()/d(x)(xln(x)−x)	ln(x)	Find the Derivative - d/dx f(x)=x natural log of x-x
d(e^(−x^3))/d(x)	−3x^2e^(−x^3)	Find the Derivative - d/dx e^(-x^3)
d(ln(x^x))/d(x)	ln(x)+1	Find the Derivative - d/dx natural log of x^x
d(ln(x^2+9))/d(x)	(2*x)/(x^2+9)	Find the Derivative - d/dx natural log of x^2+9
d()/d(x)x^2(1−9*x)	2x−27x^2	Find the Derivative - d/dx x^2(1-9x)
d()/d(x)1/√(3,x)	−1/(3√(3,x^4))	Find the Derivative - d/dx 1/( cube root of x)
d()/d(x)3(4−9*x)^4	−108(4−9x)^3	Find the Derivative - d/dx 3(4-9x)^4
d()/d(x)*(e^x+e^(−x))	e^x−e^(−x)	Find the Derivative - d/dx e^x+e^(-x)
d(tan(5*x))/d(x)	5sec^2(5x)	Find the Derivative - d/dx tan(5x)
d()/d(x)√(3,1+4*x)	4/(3√(3,(1+4*x)^2))	Find the Derivative - d/dx y = cube root of 1+4x
d()/d(x)√(,3−5*x)	−5/(2√(,3−5*x))	Find the Derivative - d/dx y = square root of 3-5x
(d(2)*sin^2(x))/d(x)	2sin(2x)	Find the Derivative - d/dx 2sin(x)^2
d()/d(x)√(4,x)	1/(4√(4,x^3))	Find the Derivative - d/dx y = fourth root of x
d()/d(x)x(x^2−8/x)	3*x^2	Find the Derivative - d/dx x(x^2-8/x)
d()/d(x)2x^2	4*x	Find the Derivative - d/dx y=2x^2
d()/d(x)x^(6cos(x))	x^(6cos(x))((6cos(x))/x−6sin(x)*ln(x))	Find the Derivative - d/dx y=x^(6cos(x))
d(ln(9*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 9x
d()/d(x)x^2sin(4*x)	4x^2cos(4x)+2xsin(4x)	Find the Derivative - d/dx y=x^2sin(4x)
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()/d(x)sin(tan(6x))	6cos(tan(6x))sec^2(6x)	Find the Derivative - d/dx y=sin(tan(6x))
d()/d(x)(5x^2−9x+13)/(2*x+4)	(5x^2+20x−31)/(2*(x+2)^2)	Find the Derivative - d/dx (5x^2-9x+13)/(2x+4)
d()/d(x)5/(x^3)	−15/(x^4)	Find the Derivative - d/dx 5/(x^3)
d()/d(x)ln(x)/(x^3)	(1−3*ln(x))/(x^4)	Find the Derivative - d/dx y=( natural log of x)/(x^3)
d()/d(x)*(log_2)(x)	1/(x*ln(2))	Find the Derivative - d/dx y = log base 2 of x
d()/d(x)8/(3*x^2)	−16/(3*x^3)	Find the Derivative - d/dx 8/(3x^2)
d()/d(x)*8^x	8^x*ln(8)	Find the Derivative - d/dx y=8^x
(d(9)*x^3)/d(x)	27*x^2	Find the Derivative - d/dx 9x^3
d(cos(tan(x)))/d(x)	−sin(tan(x))*sec^2(x)	Find the Derivative - d/dx y=cos(tan(x))
d()/d(x)4/(3*x^2)	−8/(3*x^3)	Find the Derivative - d/dx y=4/(3x^2)
d()/d(x)(x^2−3x)	2*x−3	Find the Derivative - d/dx x^2-3x
d()/d(x)ln(9x^3−x^2)	(27x−2)/(9x^2−x)	Find the Derivative - d/dx y = natural log of 9x^3-x^2
d()/d(x)(log_)(6x)	1/(x*ln(10))	Find the Derivative - d/dx y = log of 6x
d()/d(x)(2*x^2)/5	(4*x)/5	Find the Derivative - d/dx (2x^2)/5
d()/d(x)(x^2+2x+1)	2*x+2	Find the Derivative - d/dx x^2+2x+1
d()/d(x)*(4−x^2)	−2*x	Find the Derivative - d/dx y=4-x^2
d(ln(4))/d(x)	0	Find the Derivative - d/dx natural log of 4
d(sin(4*x))/d(x)	4cos(4x)	Find the Derivative - d/dx y=sin(4x)
d(sin(3*x))/d(x)	3cos(3x)	Find the Derivative - d/dx y=sin(3x)
d()/d(x)1/√(,x^9)	−9/(2*x^(11/2))	Find the Derivative - d/dx 1/( square root of x^9)
d()/d(y)(1/(y^2)−3/(y^4))(y+5*y^3)	5+14/(y^2)+9/(y^4)	Find the Derivative - d/dy (1/(y^2)-3/(y^4))(y+5y^3)
(∫_^)(e^(x^3)*d(x))	(∑_n=0^∞)((x^(3n+1))/(n!(3n+1)))+C	Find the Integral e^(x^3)
(∫_^)(cos(x^2)*d(x))	√(,π/2)C(x√(,2/π))+C	Find the Integral cos(x^2)
(∫_^)(sin(5x)d(x))	−1/5cos(5x)+C	Find the Integral sin(5x)
(∫_^)(cos^2(θ)*d(θ))	θ/2+sin(2*θ)/4+C	Find the Integral cos(theta)^2
(∫_^)(1/(x^2+1)*d(x))	arctan(x)+C	Find the Integral 1/(x^2+1)
(∫_^)(te^td(t))	t*e^t−e^t+C	Find the Integral te^t
d(√(3,x))/d(x)	1/(3√(3,x^2))	Find the Derivative Using Chain Rule - d/dx cube root of x
d()/d(x)(x/3.8+3.8/x)(x^2+1)	(3*x^2+1)/3.8+3.8−3.8/(x^2)	Find the Derivative - d/dx (x/3.8+3.8/x)(x^2+1)
tan(arccos(√(,2)/2))	1	Simplify tan(arccos(( square root of 2)/2))
(√(,x+h)−√(,x))*(√(,x+h)+√(,x))	h	Simplify
(a+h)^3	a^3+3a^2h+3ah^2+h^3	Multiply (a+h)^3
d(sin(t))/d(t)	sin(2*t)	Find the Derivative - d/dt sin(t)^2
d()/d(x)(x+2sin(x))	1+2*cos(x)	Find the Derivative - d/d@VAR f(x)=x+2sin(x)
(4x+4y)^3=64x^3+64y^3	−(2xy+y^2)/(x^2+2xy)	Find dy/dx (4x+4y)^3=64x^3+64y^3
ƒ(x)=x^4−24x^2+12x	(2,−56),(−2,−104)	Find the Inflection Points f(x)=x^4-24x^2+12x
d()/d(x)*(ln(x))^cos(x)	see full solution →	Find the Derivative - d/dx ( natural log of x)^(cos(x))
d(x^9)/d(x)	9*x^8	Find the Derivative - d/d@VAR f(x)=x^9
d(cos(x))/d(x)	−sin(x)	Find the Derivative - d/d@VAR f(x)=cos(x)
d()/d(x)*(x^3−8)^(2/3)	(2*x^2)/√(3,x^3−8)	Find the Derivative - d/d@VAR f(x)=(x^3-8)^(2/3)
(d(x^2)e^(3x))/d(x)	3x^2e^(3x)+2xe^(3x)	Find the Derivative - d/dx x^2e^(3x)
d()/d(x)x^2sin(2*x)	2x^2cos(2x)+2xsin(2x)	Find the Derivative - d/dx x^2sin(2x)
d()/d(x)(−9/((3x^2)^3))	2/(x^7)	Find the Derivative - d/dx y=-9/((3x^2)^3)
d(ln(√(,x)))/d(x)	1/(2*x)	Find the Derivative - d/dx natural log of square root of x
d(ln(1/x))/d(x)	−1/x	Find the Derivative - d/dx natural log of 1/x
d()/d(x)(2x+4)	2	Find the Derivative - d/dx 2x+4
d()/d(x)2x*ln(x)	2+2*ln(x)	Find the Derivative - d/dx 2x natural log of x
d()/d(x)*(√(,x)−2√(3,x))	1/(2√(,x))−2/(3√(3,x^2))	Find the Derivative - d/dx square root of x-2 cube root of x
d(e^1)/d(x)	0	Find the Derivative - d/dx e^1
d()/d(x)x/(x^2−9)	(−x^2−9)/((x^2−9)^2)	Find the Derivative - d/dx x/(x^2-9)
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))
d()/d(x)(3x^2−7*x−3)^2⋅16	(3x^2−7x−3)(192x−224)	Find the Derivative - d/dx (3x^2-7x-3)^2*16
d(√(,3x+2cos(x)))/d(x)	(3−2sin(x))/(2√(,3x+2*cos(x)))	Find the Derivative - d/dx square root of 3x+2cos(x)
d()/d(x)ln(x)/(x^7)	(1−7*ln(x))/(x^8)	Find the Derivative - d/dx ( natural log of x)/(x^7)
d()/d(x)*(−csc(x)−sin(x))	csc(x)*cot(x)−cos(x)	Find the Derivative - d/dx y=-csc(x)-sin(x)
d(e^(9*x))/d(x)	9e^(9x)	Find the Derivative - d/dx e^(9x)
d()/d(x)(3*x)/4	3/4	Find the Derivative - d/dx (3x)/4
d()/d(x)(ax^2+b*x+c)	2ax+b	Find the Derivative - d/dx ax^2+bx+c
d()/d(x)(d(5)*x^3)/d(x)	30*x	Find the Derivative - d/dx d/(dx)(5x^3)
d((log_9)(x))/d(x)	1/(x*ln(9))	Find the Derivative - d/dx log base 9 of x
d()/d(x)(x/3.6+3.6/x)(x^2+1)	(5*x^2)/6+349/90−3.6/(x^2)	Find the Derivative - d/dx (x/3.6+3.6/x)(x^2+1)
d(e^(10*x))/d(x)	10e^(10x)	Find the Derivative - d/dx e^(10x)
d()/d(x)(x/3.5+3.5/x)(x^2+1)	(6x^2)/7+53/14−7/(2x^2)	Find the Derivative - d/dx (x/3.5+3.5/x)(x^2+1)
d()/d(x)(−4*x)/((x^2−1)^2)	(12*x^2+4)/((x^2−1)^3)	Find the Derivative - d/dx (-4x)/((x^2-1)^2)
d()/d(x)8x^(1/2)	4*x^(−1/2)	Find the Derivative - d/dx 8x^(1/2)
d()/d(x)(x^2)/(x^2−9)	−(18*x)/((x^2−9)^2)	Find the Derivative - d/dx (x^2)/(x^2-9)
d()/d(x)4x^3	12*x^2	Find the Derivative - d/dx y=4x^3
d()/d(x)(e^x+e^(−x))/2	(e^x−e^(−x))/2	Find the Derivative - d/dx (e^x+e^(-x))/2
d()/d(x)(e^x−e^(−x))/(e^x+e^(−x))	4/((e^x+e^(−x))^2)	Find the Derivative - d/dx (e^x-e^(-x))/(e^x+e^(-x))
d()/d(x)(x^2+5x)	2*x+5	Find the Derivative - d/dx x^2+5x
d()/d(x)x^2e^x	x^2e^x+2x*e^x	Find the Derivative - d/dx y=x^2e^x
d()/d(x)(x+8)(24/x+12)	12−192/(x^2)	Find the Derivative - d/dx (x+8)(24/x+12)
d()/d(t)*(√(3,t^2)+2√(,t^3))	2/(3√(3,t))+3√(,t)	Find the Derivative - d/dt cube root of t^2+2 square root of t^3
((6y^3)^4)/(2y^9)	648*y^3	Simplify ((6y^3)^4)/(2y^9)
3x^2−12x+9=0	1, 3	Solve for x 3x^2-12x+9=0
V=4/3πr^3	(4πr^3)/3	Solve for V V=4/3*(pr^3)
e^(−x)=0	0⇒No solution	Solve for x e^(-x)=0
d()/d(x)(x^2−5x+2)(5x^3−x^2+5)	25x^4−104x^3+45x^2+6x−25	Find the Derivative - d/dx (x^2-5x+2)(5x^3-x^2+5)
ln(ln(x))	ln(ln(x))	Evaluate natural log of natural log of x
y=ln(7*x)	ln(7*x)	Graph natural log of 7x
x=ln(y)	e^x	Graph natural log of y
(lim_x→−1)((x^2+2*x+1)/(x^4−1))	0	Evaluate the Limit
y=x^3−4*x,(2,0)	8*x−16	Find the Tangent Line at the Point y=x^3-4x , (2,0)
(lim_x→0)((√(,x+5)−√(,5))/x)	√(,5)/10	Evaluate the Limit
(lim_x→0)((1−cos(x))/sin(x))	0	Evaluate the Limit
(lim_x→0)((1−cos(x))/(x^2))	1/2	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→7)((√(,x+2)−3)/(x−7))	1/6	Evaluate the Limit
y=x,y=√(6,x)	5/14	Find the Area Between the Curves y=x , y = sixth root of x
(lim_x→−8)((x^2−64)/(x+8))	−16	Evaluate the Limit
(lim_x→1)(cos((π*x)/3))	1/2	Evaluate the Limit limit as x approaches 1 of cos((pix)/3)
(lim_x→−1)(5)	5	Evaluate the Limit limit as x approaches -1 of 5
(lim_x→0)(5)	5	Evaluate the Limit limit as x approaches 0 of 5
(lim_x→0)(sec(2*x))	1	Evaluate the Limit limit as x approaches 0 of sec(2x)
(lim_x→2)((x^3−8)/(x^2−4))	3	Evaluate the Limit
(lim_x→3)((1/x−1/3)/(x−3))	−1/9	Evaluate the Limit
(lim_x→0)(100/(50*x+1))	100	Evaluate the Limit limit as x approaches 0 of 100/(50x+1)
(lim_x→5)((x^2−3*x−10)/(x−5))	7	Evaluate the Limit
(lim_x→5)((x-5)/(x-5))	1	Evaluate the Limit
(lim_x→3)((x-3)/(x-3))	1	Evaluate the Limit
(lim_x→4)((x-4)/(x-4))	1	Evaluate the Limit
(lim_x→16)((√(,x)−4)/(x−16))	1/8	Evaluate the Limit
(lim_x→16)((x−16)/(√(,x)−4))	8	Evaluate the Limit
(lim_x→π/2)(sec(x)−tan(x))	0	Evaluate the Limit
(∫_^)(sin(x)*d(x))	−cos(x)+C	Find the Antiderivative f(x)=sin(x)
(∫_^)(1/(x^2)*d(x))	−1/x+C	Find the Antiderivative f(x)=1/(x^2)
(∫_^)(e^(x/2)*d(x))	2*e^(x/2)+C	Find the Antiderivative e^(x/2)
d()/d(x)x^9cos(x)	x^8(9cos(x)−x*sin(x))	Find the Derivative - d/dx x^9cos(x)
(∫_^)(e^(x^2)*d(x))	√(,π)/2*erfi(x)+C	Find the Antiderivative e^(x^2)
(∫_^)(8xd(x))	4*x^2+C	Find the Antiderivative 8x
(∫_^)(2e^xd(x))	2*e^x+C	Find the Antiderivative 2e^x
ƒ(x)=x/(x^2+9)	see full solution →	Find the Local Maxima and Minima f(x)=x/(x^2+9)
d()/d(x)4/(x^2)	−8/(x^3)	Find the Derivative - d/d@VAR f(x)=4/(x^2)
d(tan(x))/d(x)	sec^2(x)	Find the Derivative - d/d@VAR f(x)=tan(x)
d()/d(x)8x^2	16*x	Find the Derivative - d/d@VAR f(x)=8x^2
d(sin(x))/d(x)	2sin(x)cos(x)	Find the Derivative - d/d@VAR f(x)=sin(x)^2
ƒ(x)=x+49/x	see full solution →	Find the Local Maxima and Minima f(x)=x+49/x
d()/d(x)d(x^3)/d(x)	6*x	Find the Derivative - d/dx d/(dx)(x^3)
ƒ(x)=x^4−8*x^3	Local Minimum: *(6,−432), Local Maxima: None	Find the Local Maxima and Minima f(x)=x^4-8x^3
ƒ(x)=2x^3+3x^2−12*x	see full solution →	Find the Local Maxima and Minima f(x)=2x^3+3x^2-12x
(∫_^)(te^(−9t)*d(t))	−1/9te^(−9t)−1/81e^(−9*t)+C	Evaluate the Integral integral of te^(-9t) with respect to t
(lim_x→4)((x^2−4x)/(x^2−3x−4))	4/5	Evaluate the Limit
(lim_x→3)(x^2)	9	Evaluate the Limit limit as x approaches 3 of x^2
(lim_x→2)((2−x)/(x^2−4))	−1/4	Evaluate the Limit limit as x approaches 2 of (2-x)/(x^2-4)
(lim_x→0)(cos(1/x))	Does Not Exist	Evaluate the Limit limit as x approaches 0 of cos(1/X)
(lim_x→∞)(√(,25x^2+x)−5x)	1/10	Evaluate the Limit
(lim_x→5)((x^2−5*x+6)/(x−5))	Does Not Exist	Evaluate the Limit
(lim_x→16)((√(,x)−4)/(x−16))	1/8	Evaluate the Limit
(∫_4^5)((x^3−3x^2−9)/(x^3−3x^2)*d(x))	23/20+ln(5/8)	Evaluate the Integral
sec(x)	1/cos(x)	Graph sec(x)
d()/d(x)(2x^3−5x) at *(1,−3)	1	Evaluate the Derivative at @POINT y=2x^3-5x , (1,-3)
arctan(−√(,3))	−π/3	Evaluate arctan(- square root of 3)
ƒ(x)=x^4−2*x^3	0,3/2	Find the Critical Points f(x)=x^4-2x^3
ƒ(x)=x^4−4*x^3+10	0, 3	Find the Critical Points f(x)=x^4-4x^3+10
ƒ(x)=3x^(2/3)−2x	x=0, x = 1	Find the Critical Points f(x)=3x^(2/3)-2x
ƒ(x)=(x^2−4)^(2/3)	−2,0,2	Find the Critical Points f(x)=(x^2-4)^(2/3)
x*y=32	−y/x	Find dy/dx xy=32
sin((7*π)/4)	−√(,2)/2	Evaluate sin((7pi)/4)
sec(π/3)*tan(π/3)	2√(,3)	Evaluate sec(pi/3)tan(pi/3)
arctan(0)	0	Evaluate arctan(0)
y=x^2+2*x	−1	Find the Horizontal Tangent Line y=x^2+2x
x^2+y^2=−18*x	9, y = -9	Find the Horizontal Tangent Line x^2+y^2=-18x
x^2+y^2=−16*x	8, y = -8	Find the Horizontal Tangent Line x^2+y^2=-16x
ƒ(x)=x^4−6*x^2	(1,−5),(−1,−5)	Find the Inflection Points f(x)=x^4-6x^2
d()/d(x)1/x	−1/(x^2)	Use the Limit Definition to Find the Derivative 1/x
d(x^2)/d(x)	2*x	Use the Limit Definition to Find the Derivative x^2
g(x)=9−x^2	−2*x	Use the Limit Definition to Find the Derivative g(x)=9-x^2
(lim_x→−1)((x^2−4x)/(x^2−3x−4))	Does Not Exist	Evaluate the Limit
d(√(,x))/d(x)	1/(2√(,x))	Find the Derivative - d/dx square root of x
d()/d(x)(4*x)/((x^2+1)^2)	(4−12*x^2)/((x^2+1)^3)	Find the Derivative - d/dx (4x)/((x^2+1)^2)
(∑_i=1^8)(2^(i−1))	255	Evaluate the Summation sum from i=1 to 8 of 2^(i-1)
d()/d(x)5/(3*x)	−5/(3*x^2)	Find the Derivative - d/dx 5/(3x)
d()/d(x)(5x^2−x^3)	10x−3x^2	Find the Derivative - d/dx 5x^2-x^3
d()/d(x)(∫_^)(5x*d(x))	5*x	Find the Derivative of the Integral integral of 5x with respect to x
(lim_x→2)(√(,(5x^2+5)/(9x−2)))	5/4	Evaluate the Limit
(∫_^)(x√(3,6x+7)d(x))	((6x+7)^(7/3))/84−(7(6*x+7)^(4/3))/48+C	Evaluate the Integral
−(3(−3)^2(−5))/(2*(−3)^3−(−5))	−135/49	Evaluate -(3(-3)^2(-5))/(2(-3)^3-(-5))
(∫_1^8)(1/(x^3)*d(x))	63/128	Evaluate the Integral
(∫_^)(5x^2d(x))	(5*x^3)/3+C	Evaluate the Integral integral of 5x^2 with respect to x
(∫_^)(1/u*d(u))	ln(u)	Evaluate the Integral
(∫_^)(1/y*d(y))	ln(y)	Evaluate the Integral
(∫_^)(ln(4x−3)d(x))	(x−3/4)ln(4x−3)−x+C	Evaluate the Integral
(∫_0^7)(√(,y+9)*d(y))	74/3	Evaluate the Integral
(∫_0^ln(2))(e^x*d(x))	1	Evaluate the Integral
(∫_0^1)(xe^xd(x))	1	Evaluate the Integral
(∫_0^1)(3xd(x))	3/2	Evaluate the Integral
(∫_0^√(,3))((4x)/√(,x^2+1)d(x))	4	Evaluate the Integral
(∫_0^1)(x^2+√(,x)*d(x))	1	Evaluate the Integral
(∫_^)(xe^(5x)*d(x))	1/5xe^(5x)−1/25e^(5*x)+C	Evaluate the Integral integral of xe^(5x) with respect to x
(∫_^)(xln(x)d(x))	(x^2*ln(x))/2−(x^2)/4+C	Evaluate the Integral integral of x log of x with respect to x
(∫_^)(9θcos(θ)*d(θ))	9θsin(θ)+9*cos(θ)+C	Evaluate the Integral
(∫_^)(xtan(x)d(x))	see full solution →	Evaluate the Integral integral of xtan(x) with respect to x
(∫_^)(sec(3x)tan(3x)d(x))	1/3sec(3x)+C	Evaluate the Integral
(∫_^)(sec(4x)tan(4x)d(x))	1/4sec(4x)+C	Evaluate the Integral
(∫_^)(sin(8x)d(x))	−1/8cos(8x)+C	Evaluate the Integral integral of sin(8x) with respect to x
(∫_^)(ln(4x+1)d(x))	(x+1/4)ln(4x+1)−x+C	Evaluate the Integral
(∫_^)(sin(πx)d(x))	−cos(π*x)/π+C	Evaluate the Integral integral of sin(pix) with respect to x
(∫_1^5)(w^2ln(w)d(w))	125/3*ln(5)−124/9	Evaluate the Integral
(∫_^)(e^u*d(u))	e^u+C	Evaluate the Integral integral of e^u with respect to u
(∫_^)(4x^2d(x))	(4*x^3)/3+C	Evaluate the Integral integral of 4x^2 with respect to x
(∫_^)(9z√(,3z^2−7)*d(z))	(3*z^2−7)^(3/2)+C	Evaluate the Integral
(∫_^)(1/(x^2√(,4−x^2))*d(x))	−√(,4−x^2)/(4*x)+C	Evaluate the Integral
(∫_^)(2cos(x)d(x))	2*sin(x)+C	Evaluate the Integral integral of 2cos(x) with respect to x
(∫_^)(arctan(8t)d(t))	tarctan(8t)−1/16ln(1+64t^2)+C	Evaluate the Integral integral of arctan(8t) with respect to t
(∫_^)(3sin(x)d(x))	−3*cos(x)+C	Evaluate the Integral integral of 3sin(x) with respect to x
(∫_^)(xe^(x/2)d(x))	2xe^(x/2)−4*e^(x/2)+C	Evaluate the Integral integral of xe^(x/2) with respect to x
(∫_0^3)(√(,17)*d(x))	3√(,17)	Evaluate the Integral
(∫_^)(x^3cos(x)d(x))	x^3sin(x)+3x^2cos(x)−6xsin(x)−6cos(x)+C	Evaluate the Integral integral of x^3cos(x) with respect to x
(∫_^)(x^(−3/2)*d(x))	−2*x^(−1/2)+C	Evaluate the Integral integral of x^(-3/2) with respect to x
(∫_^)(ln(8x)/xd(x))	((ln(8*x))^2)/2+C	Evaluate the Integral
(∫_^)(e^cos(x)sin(x)d(x))	−e^cos(x)+C	Evaluate the Integral
(∫_^)(ln(√(3,x))*d(x))	(x*ln(x)−x)/3+C	Evaluate the Integral
8(∫_0^1)(x^3√(,1−x^2)d(x))	16/15	Evaluate the Integral
(∫_^)((5x+2)/(2x^2+7x−4)d(x))	1/2ln(abs(2x-1))+2*ln(abs(x+4))+C	Evaluate the Integral
(∫_π/4^π)(sin(x)*d(x))	1+√(,2)/2	Evaluate the Integral
(∫_^)(1/√(,1−4x^2)d(x))	1/2arcsin(2x)+C	Evaluate the Integral
(∫_^)(12/√(,x)*d(x))	24√(,x)+C	Evaluate the Integral
(∫_^)(cos(1/x)/(x^2)*d(x))	−sin(1/x)+C	Evaluate the Integral
(∫_^)(cos(ln(x))/x*d(x))	sin(ln(x))+C	Evaluate the Integral
(∫_^)((t^3)/√(,1−t^8)*d(t))	1/4*arcsin(t^4)+C	Evaluate the Integral
(∫_^)((2x−1)ln(7x)d(x))	(x^2−x)ln(7x)−(x^2)/2+x+C	Evaluate the Integral
(∫_^)((x^2)/2*d(x))	(x^3)/6+C	Evaluate the Integral integral of (x^2)/2 with respect to x
(∫_^)((5x^5+5x^2+10)/(x^3−x)*d(x))	5/3x^3+5x-10ln(abs(x))+10ln(abs(x-1))+5*ln(abs(x+1))+C	Evaluate the Integral
(∫_^)((x^2+8x)cos(x)*d(x))	(x^2+8x−2)sin(x)+(2x+8)cos(x)+C	Evaluate the Integral
(∫_1^7)(ln(x)/(x^3)*d(x))	(24−ln(7)−ln(7))/98	Evaluate the Integral
(∫_0^4π)(t^2sin(2t)d(t))	−8*π^2	Evaluate the Integral
(∫_^)((x^2−5x)e^x*d(x))	(x^2−7x+7)e^x+C	Evaluate the Integral
(∫_^)(x^2−9x+2d(x))	(x^3)/3−(9x^2)/2+2x+C	Evaluate the Integral integral of x^2-9x+2 with respect to x
(∫_0^1)((x^2+8)e^(−x)d(x))	10−13/e	Evaluate the Integral
(∫_^)((e^t+1)^2*d(t))	1/2e^(2t)+2*e^t+t+C	Evaluate the Integral integral of (e^t+1)^2 with respect to t
(∫_^)(sec(x)tan(x)d(x))	sec(x)+C	Evaluate the Integral
(∫_^)(x^(−1/2)*d(x))	2*x^(1/2)+C	Evaluate the Integral integral of x^(-1/2) with respect to x
(lim_x→0)(1−2*x)	e^(−2)	Evaluate Using L'Hospital's Rule limit as x approaches 0 of (1-2x)^(1/x)
(∑_i=1^20)(i−1)	2470	Evaluate the Summation sum from i=1 to 20 of (i-1)^2
(lim_x→81)((√(,x)−9)/(x−81))	1/18	Evaluate the Limit
d^2(e^(2*x))/(d(x)^2)	4e^(2x)	Find the 2nd Derivative e^(2x)
d()/d(x)x(7+2*x)	7 + 4x	Find the Derivative - d/dx x(7+2x)
d()/d(x)1/(x^8)	−8/(x^9)	Find the Derivative - d/dx y=1/(x^8)
d()/d(x)√(5,x^2)	2/(5√(5,x^3))	Find the Derivative - d/dx fifth root of x^2
d()/d(x)(8x−x^2)	8 - 2x	Find the Derivative - d/dx y=8x-x^2
d(cos(a^7+x^7))/d(x)	−7x^6sin(a^7+x^7)	Find the Derivative - d/dx cos(a^7+x^7)
(lim_a→−2)(F(a))	F*(−2)	Evaluate the Limit limit as a approaches -2 of F(a)
d(√(4,x^5))/d(x)	(5√(4,x))/4	Find the Derivative - d/dx fourth root of x^5
(2x+2y)^3=8x^3+8y^3	−(2xy+y^2)/(x^2+2xy)	Find dy/dx (2x+2y)^3=8x^3+8y^3
xy+x+y=x^2y^2	(2xy^2−y−1)/(x+1−2x^2y)	Find dy/dx xy+x+y=x^2y^2
(lim_x→8)(x)*sin(2/x)	8*sin(1/4)	Evaluate the Limit limit as x approaches 8 of xsin(2/x)
(lim_x→−6)((x^2−36)/(x+6))	−12	Evaluate the Limit
(lim_x→−3)((x^3+27)/(x+3))	27	Evaluate the Limit
(lim_x→3)((x−3)/(x^2−9))	1/6	Evaluate the Limit limit as x approaches 3 of (x-3)/(x^2-9)
(lim_x→−3)(ƒ(x))	ƒ*(−3)	Evaluate the Limit limit as x approaches -3 of f(x)
ƒ(x)=2x^3−3x^2−12*x	see full solution →	Find the Local Maxima and Minima f(x)=2x^3-3x^2-12x
ƒ(x)=3x^5−5x^3	see full solution →	Find the Local Maxima and Minima f(x)=3x^5-5x^3
ƒ(x)=x^4−12*x^3	see full solution →	Find the Local Maxima and Minima f(x)=x^4-12x^3
ƒ(x)=x^3−3*x+2	see full solution →	Find the Local Maxima and Minima f(x)=x^3-3x+2
ƒ(x)=x*e^(−x^2)	see full solution →	Find the Local Maxima and Minima f(x)=xe^(-x^2)
(lim_x→64)((√(,x)−8)/(x−64))	1/16	Evaluate the Limit
ƒ(x)=(x−3)(x^2−6x−18)	see full solution →	Find the Domain and Range f(x)=(x-3)(x^2-6x-18)
d()/d(x)*(3√(,x)+5)	3/(2√(,x))	Find the Derivative - d/d@VAR f(x)=3 square root of x+5
x^3−12*x	see full solution →	Find the Local Maxima and Minima x^3-12x
(∫_^)(5xd(x))	(5*x^2)/2+C	Find the Antiderivative 5x
g(x)^′=3x^2−2x−4	x^3−x^2−4*x+C	Find the Function g'(x)=3x^2-2x-4
(∫_^)(1/√(,x)*d(x))	2√(,x)+C	Find the Antiderivative 1/( square root of x)
(lim_x→9)((3−√(,x))/(9*x−x^2))	1/54	Evaluate the Limit
(lim_x→∞)(√(,49x^2+x)−7x)	1/14	Evaluate the Limit
(lim_x→0)(1+x)	e^8	Evaluate the Limit limit as x approaches 0 of (1+x)^(8/x)
(lim_x→25)((5−√(,x))/(25*x−x^2))	1/250	Evaluate the Limit
(lim_x→16)((4−√(,x))/(x−16))	−1/8	Evaluate the Limit
(lim_x→1)((x^3−1)/(x−1))	3	Evaluate the Limit
(lim_x→−1)((x^2−1)/(x+1))	−2	Evaluate the Limit
(lim_x→−1)((x^2−4x)/(x^2−3x−4))	Does Not Exist	Evaluate the Limit
(lim_x→4)((x^3−64)/(x−4))	48	Evaluate the Limit
(lim_x→4)((x−4)/(x^2−16))	1/8	Evaluate the Limit
(lim_x→4)((x−4)/(x^2−3*x−4))	1/5	Evaluate the Limit
(lim_x→−2)((x+2)/(x^3+8))	1/12	Evaluate the Limit
(lim_x→5)((x^2−5*x+6)/(x−5))	Does Not Exist	Evaluate the Limit
(lim_x→9)((x−9)/(√(,x)−3))	6	Evaluate the Limit
(lim_x→4)((2−√(,x))/(4*x−x^2))	1/16	Evaluate the Limit
(lim_x→3)(x/(x−3))	Does Not Exist	Evaluate the Limit limit as x approaches 3 of x/(x-3)
(lim_x→0)((√(,4+x)−2)/x)	1/4	Evaluate the Limit
(lim_x→1)((x−1)/(√(,x)−1))	2	Evaluate the Limit
(lim_x→1)((x^4−1)/(x^3−1))	4/3	Evaluate the Limit
( \lim_{x \to -6} \frac{2x+12}{	x+6	} )
(lim_x→−9)((x^2−81)/(x+9))	−18	Evaluate the Limit
(lim_x→0)(sin(x)/(2*x^2−x))	−1	Evaluate the Limit
(lim_x→0^+)(sin(x))*ln(x)	0	Evaluate the Limit
(lim_x→4)(ƒ(x))	ƒ(4)	Evaluate the Limit limit as x approaches 4 of F(x)
(lim_x→0)(cot(x))	Does Not Exist	Evaluate the Limit limit as x approaches 0 of cot(x)
(lim_x→0)(2)	2	Evaluate the Limit limit as x approaches 0 of 2
(lim_x→0)(x^2)*sin(1/x)	0	Evaluate the Limit limit as x approaches 0 of x^2sin(1/x)
(lim_x→5)((x−5)/(x^2−25))	1/10	Evaluate the Limit
(lim_x→1)(x/ln(x))	Does Not Exist	Evaluate the Limit
(lim_x→1)((2−x)/((x−1)^2))	∞	Evaluate the Limit
(lim_x→0)((√(,2+x)−√(,2))/x)	√(,2)/4	Evaluate the Limit
(lim_x→−1)(1/(x+1))	Does Not Exist	Evaluate the Limit limit as x approaches -1 of 1/(x+1)
(lim_x→1)((1/x−1)/(x−1))	−1	Evaluate the Limit limit as x approaches 1 of (1/x-1)/(x-1)
(lim_x→−2)(F(x))	F*(−2)	Evaluate the Limit limit as x approaches -2 of F(x)
(lim_t→∞)(√(,t+t^2)/(2*t−t^2))	0	Evaluate the Limit
(lim_x→∞)(√(,36x^2+x)−6x)	1/12	Evaluate the Limit
(lim_x→7)((x^2−49)/(x−7))	14	Evaluate the Limit
(lim_x→∞)(√(,81x^2+x)−9x)	1/18	Evaluate the Limit
(lim_x→5)((x+1)/(x−5))	Does Not Exist	Evaluate the Limit limit as x approaches 5 of (x+1)/(x-5)
(lim_x→1)((√(,x)−x^2)/(1−√(,x)))	3	Evaluate the Limit
y=x,y=√(4,x)	3/10	Find the Area Between the Curves y=x , y = fourth root of x
y=x+12,y=x^2	343/6	Find the Area Between the Curves y=x+12 , y=x^2
y=1/2*x^2,y=−x^2+6	16	Find the Area Between the Curves y=1/2x^2 , y=-x^2+6
y=x^2+2*x−4,y=x+4	(11√(,33))/2	Find the Area Between the Curves y=x^2+2x-4 , y=x+4
y=x^2+9*x−4,y=x+2	(88√(,22))/3	Find the Area Between the Curves y=x^2+9x-4 , y=x+2
y=x^2−5*x+4,y=−(x−1)^2	9/8	Find the Area Between the Curves y=x^2-5x+4 , y=-(x-1)^2
y=x^2+6,(1,7)	2*x+5	Find the Tangent Line at the Point y=x^2+6 , (1,7)
(lim_x→0)(sin(x)/(5*x))	1/5	Evaluate the Limit
y=x^3−3*x,(2,2)	9*x−16	Find the Tangent Line at the Point y=x^3-3x , (2,2)
(lim_h→0)(((4+h)^2−16)/h)	8	Evaluate the Limit
ln(8)	ln(8)≈2.079	Graph natural log of 8
(lim_x→∞)(ln(x))	∞	Evaluate natural log of infinity
ln(tan(x))	ln(tan(x))	Graph natural log of tan(x)
y=ln(8*x)	ln(8*x)	Graph natural log of 8x
ln(cos(x))	ln(cos(x))	Graph natural log of cos(x)
y=ln(4*x)	ln(4*x)	Graph natural log of 4x
2*ln(2)	ln(4)	Evaluate 2 natural log of 2
tan(x)=−1/3	see full solution →	Solve for x tan(x)=-1/3
q=9000−100*p	90 - 0.01q	Solve for p q=9000-100p
144pr−6p^2r^2=0	0,24/p	Solve for r 144pr-6p^2r^2=0
ln(x^2−1)=3	3⇒x=±√(,e^3+1)	Solve for x natural log of x^2-1=3
3x^2−2x−1=0	1,−1/3	Solve for x 3x^2-2x-1=0
12x^2−136x+289=0	17/2,17/6	Solve for x 12x^2-136x+289=0
2*ln(x)=1	1⇒x=√(,e)	Solve for x 2 natural log of x=1
9x^2−6x−3=0	1,−1/3	Solve for x 9x^2-6x-3=0
(x^(3/2))/(3/2)	(2*x^(3/2))/3	Simplify (x^(3/2))/(3/2)
(e^(−x))^2	e^(−2*x)	Simplify (e^(-x))^2
x(22−2x)(22−2x)	4x^3−88x^2+484*x	Simplify (x)(22-2x)(22-2x)
(−2x^5y^3)(3x^(−1)*y^5)	−6x^4y^8	Simplify (-2x^5y^3)*(3x^-1y^5)
−3x−4y=−2	−2⇒x=(2−4*y)/3	Solve for x -3x-4y=-2
2*(x+h)^3	2x^3+6x^2h+6xh^2+2h^3	Simplify 2(x+h)^3
1−1/95*x^2	(95−x^2)/95	Simplify 1-1/95x^2
cos(x)⋅cos(x)	cos^2(x)	Simplify cos(x)*cos(x)
d()/d(t)*t√(,4−t)	(8−3*t)/(2√(,4−t))	Find the Derivative - d/dt t square root of 4-t
d()/d(t)2t	2	Find the Derivative - d/dt 2t
d()/d(x)9e^x*cos(x)	9e^x(cos(x)−sin(x))	Find the Derivative - d/dx 9e^xcos(x)
d()/d(x)1/sec(x)	−sin(x)	Find the Derivative - d/dx 1/(sec(x))
d()/d(x)√(5,x^4)	4/(5√(5,x))	Find the Derivative - d/dx fifth root of x^4
d()/d(x)1/(x^2−4)	(−2*x)/((x^2−4)^2)	Find the Derivative - d/dx 1/(x^2-4)
d()/d(x)π/((3*x)^2)	−(2π)/(9x^3)	Find the Derivative - d/dx y=pi/((3x)^2)
d()/d(x)1/(3*x^3)	−1/(x^4)	Find the Derivative - d/dx 1/(3x^3)
d()/d(x)10e^x	10*e^x	Find the Derivative - d/dx 10e^x
d()/d(x)√(3,8/x)	−2/(3*x√(3,x))	Find the Derivative - d/dx cube root of 8/x
d()/d(x)*(x^2+6)	2*x	Find the Derivative - d/dx x^2+6
d(4*x−x^2)/d(x)	200(2−x)(4*x−x^2)^99	Find the Derivative - d/dx (4x-x^2)^100
d()/d(x)(e^x)/(x^3)	(e^x*(x−3))/(x^4)	Find the Derivative - d/dx (e^x)/(x^3)
d()/d(x)*(x−x^2)	1 - 2x	Find the Derivative - d/dx x-x^2
d(arctan(e^x))/d(x)	(e^x)/(1+e^(2*x))	Find the Derivative - d/dx arctan(e^x)
d()/d(x)√(5,x^6)	(6√(5,x))/5	Find the Derivative - d/dx fifth root of x^6
d(e^(7*x^2+3))/d(x)	14xe^(7*x^2+3)	Find the Derivative - d/dx e^(7x^2+3)
d()/d(x)cot(x)/(1+cot(x))	−csc^2(x)/((1+cot(x))^2)	Find the Derivative - d/dx (cot(x))/(1+cot(x))
d(sin(x^2))/d(x)	2xcos(x^2)	Find the Derivative - d/dx y=sin(x^2)
d(√(,x−4))/d(x)	1/(2√(,x−4))	Find the Derivative - d/dx square root of x-4
d(√(,ln(x)))/d(x)	1/(2*x√(,ln(x)))	Find the Derivative - d/dx square root of natural log of x
d()/d(x)sec(x)/(1+sec(x))	(sec(x)*tan(x))/((1+sec(x))^2)	Find the Derivative - d/dx (sec(x))/(1+sec(x))
d(√(3,x^2−1))/d(x)	(2*x)/(3√(3,(x^2−1)^2))	Find the Derivative - d/dx cube root of x^2-1
d()/d(x)x/(x^2+64)	(64−x^2)/((x^2+64)^2)	Find the Derivative - d/dx x/(x^2+64)
d(10^x)/d(x)	10^x*ln(10)	Find the Derivative - d/dx 10^x
d()/d(x)x^4e^x	x^3e^x(x+4)	Find the Derivative - d/dx y=x^4e^x
d()/d(x)(6x−x^2)	6 - 2x	Find the Derivative - d/dx y=6x-x^2
d()/d(x)*3√(,x^5)	(15√(,x^3))/2	Find the Derivative - d/dx 3 square root of x^5
(d(2)*x^5)/d(x)	10*x^4	Find the Derivative - d/dx 2x^5
d()/d(x)x^2(1−8*x)	2x−24x^2	Find the Derivative - d/dx x^2(1-8x)
d()/d(x)3x(6x−5*x^2)	36x−45x^2	Find the Derivative - d/dx y=3x(6x-5x^2)
d()/d(x)(3x+2)	3	Find the Derivative - d/dx 3x+2
d()/d(x)5e^x√(,x)	5e^x√(,x)+(5e^x)/(2√(,x))	Find the Derivative - d/dx 5e^x square root of x
(d(−)4x)/d(x)	−4	Find the Derivative - d/dx -4x
d()/d(x)(3x−x^2)	3 - 2x	Find the Derivative - d/dx 3x-x^2
d(x−1)/d(x)	3*(x−1)^2	Find the Derivative - d/dx (x-1)^3
d()/d(x)(x/3.2+3.2/x)(x^2+1)	0.9375*x^2+3.5125−3.2/(x^2)	Find the Derivative - d/dx (x/3.2+3.2/x)(x^2+1)
(d(−)xe^x)/d(x)	−e^x*(x+1)	Find the Derivative - d/dx -xe^x
d()/d(x)(x−1)/x	1/(x^2)	Find the Derivative - d/dX (X-1)/X
d()/d(x)*(x−x^3)	1−3*x^2	Find the Derivative - d/dx y=x-x^3
d(x−2)/d(x)	3*(x−2)^2	Find the Derivative - d/dx (x-2)^3
d()/d(x)*(ln(x))^5	(5*(ln(x))^4)/x	Find the Derivative - d/dx ( natural log of x)^5
d()/d(x)√(3,x^2)	2/(3√(3,x))	Find the Derivative - d/dx y = cube root of x^2
d()/d(x)(x^2−8ln(x))	2*x−8/x	Find the Derivative - d/dx x^2-8 natural log of x
d()/d(x)*2^x	2^x*ln(2)	Find the Derivative - d/dx y=2^x
d()/d(x)sin(x)/cos(x)	sec^2(x)	Find the Derivative - d/dx (sin(x))/(cos(x))
(lim_x→−∞)(x+√(,x^2+8*x))	−4	Evaluate the Limit
d()/d(x)*(√(,x)−5√(3,x))	1/(2√(,x))−5/(3√(3,x^2))	Find the Derivative - d/d@VAR F(x) = square root of x-5 cube root of x
d(a^x)/d(a)	x*a^(x−1)	Find the Derivative - d/da a^x
d()/d(t)t^2sin(t)	t^2cos(t)+2t*sin(t)	Find the Derivative - d/dt t^2sin(t)
d()/d(t)(at^2+b*t+c)	2at+b	Find the Derivative - d/dt (at^2+bt+c)
d()/d(t)*sin(e^sin(t))	see full solution →	Find the Derivative - d/dt sin(e^(sin(t)^2))^2
d(e^(3tsin(2*t)))/d(t)	e^(3tsin(2t))(3sin(2t)+6tcos(2*t))	Find the Derivative - d/dt e^(3tsin(2t))
(2*(x+2)^(1/2))/((x−2)^(1/2))/((x+2)^2)	(2*(x+2)^(5/2))/((x−2)^(1/2))	Simplify (2(x+2)^(1/2))/(((x-2)^(1/2))/((x+2)^2))
√(,x−1)/(x−1)	1/√(,x−1)	Simplify ( square root of x-1)/(x-1)
(√(,x^2+9)−5)/(x+4)	(x−4)/(√(,x^2+9)+5)	Simplify ( square root of x^2+9-5)/(x+4)
2*x+cos(x)=0	x≈−0.4501836	Find the Roots (Zeros) 2x+cos(x)=0
d(S)/d(A)* where S=180A−0.30*A^3	180−0.90*A^2	Find dS/dA s=180A-0.30A^3
(∫_^)(2/(x^2)*d(x))	−2/x+C	Find the Integral 2/(x^2)
(∫_^)(e^(3x)d(x))	(e^(3*x))/3+C	Find the Integral e^(3x)
(∫_^)(x^2e^xd(x))	e^x(x^2−2x+2)+C	Find the Integral x^2e^x
d()/d(x)*x√(,4−x)	(8−3*x)/(2√(,4−x))	Find the Derivative - d/dx y=x square root of 4-x
d()/d(x)sin(x)tan(x)	sin(x)*sec^2(x)+sin(x)	Find the Derivative - d/dx y=sin(x)tan(x)
d(5^x)/d(x)	5^x*ln(5)	Find the Derivative - d/dX 5^X
d(e^(x*y))/d(y)	xe^(xy)	Find the Derivative - d/dy e^(xy)
d()/d(z)(π/2sin(x)−cos(x))	0	Find the Derivative - d/dZ y=pi/2*sin(x)-cos(x)
d()/d(x)((x^3)/3+1/(4x))	x^2−1/(4*x^2)	Find the Derivative - d/dx (x^3)/3+1/(4x)
d(ln(x^5))/d(x)	5/x	Find the Derivative - d/dx natural log of (x)^5
d()/d(x)x^2(x−2)^4	2x(x−2)^3(3x−2)	Find the Derivative - d/dx x^2(x-2)^4
d()/d(x)ln(3x)	1/x	Find the Derivative - d/dx y = log of 3x
d()/d(x)(log_)(2x)	1/(x*ln(10))	Find the Derivative - d/dx y = log of 2x
d()/d(x)*sin(√(,x))	cos(√(,x))/(2√(,x))	Find the Derivative - d/dx y=sin( square root of x)
d()/d(x)ln(9x)	1/x	Find the Derivative - d/dx y = natural log of 9x
d()/d(x)*ln((1+e^x)/(1−e^x))	(2e^x)/(1−e^(2x))	Find the Derivative - d/dx y = natural log of (1+e^x)/(1-e^x)
d()/d(x)*e^tan(x)	e^tan(x)*sec^2(x)	Find the Derivative - d/dx y=e^(tan(x))
d()/d(x)*(x^2+3)	2*x	Find the Derivative - d/dx y=x^2+3
d()/d(x)x^3ln(x)	x^2(1+3ln(x))	Find the Derivative - d/dx y=x^3 natural log of x
d(sin(x^5))/d(x)	5x^4cos(x^5)	Find the Derivative - d/dx sin(x^5)
d()/d(x)x^5e^x	x^4e^x(x+5)	Find the Derivative - d/dx y=x^5e^x
d()/d(x)(7x^2−9x+13)/(2*x+4)	(7x^2+28x−31)/(2*(x+2)^2)	Find the Derivative - d/dx (7x^2-9x+13)/(2x+4)
d(arcsin(2*x+1))/d(x)	2/√(,−4x^2−4x)	Find the Derivative - d/dx arcsin(2x+1)
d()/d(x)*2^(3^(x^2))	2xln(2)ln(3)2^(3^(x^2))*3^(x^2)	Find the Derivative - d/dx y=2^(3^(x^2))
d()/d(x)(2x^3+9*x)^5	5(2x^3+9x)^4(6*x^2+9)	Find the Derivative - d/dx y=(2x^3+9x)^5
(d(3)*tan(x))/d(x)	3*sec^2(x)	Find the Derivative - d/dx 3tan(x)
d()/d(x)1/2*x^(−1/2)	−1/4*x^(−3/2)	Find the Derivative - d/dx 1/2x^(-1/2)
d(ln(10*x))/d(x)	1/x	Find the Derivative - d/dx natural log of 10x
d(ln(3*x^2))/d(x)	2/x	Find the Derivative - d/dx natural log of 3x^2
d()/d(x)*(−cos(x))	sin(x)	Find the Derivative - d/dx f(x)=-cos(x)
d()/d(x)(4/(x^2)−10x^3)	−8/(x^3)−30*x^2	Find the Derivative - d/d@VAR f(x)=4/(x^2)-10x^3
(lim_x→225)((√(,x)−15)/(x−225))	1/30	Evaluate the Limit
d(sin(2*x))/d(x)	2cos(2x)	Find the Derivative - d/dx f(x)=sin(2x)
d(sin(3*x))/d(x)	3cos(3x)	Find the Derivative - d/dx f(x)=sin(3x)
d()/d(x)(x^3)/6	(x^2)/2	Find the Derivative - d/dx (x^3)/6
d()/d(x)(3x^2−4*x+1)	6*x−4	Find the Derivative - d/dx 3x^2-4x+1
d()/d(x)(x^3−3x+1)	3*x^2−3	Find the Derivative - d/dx y=x^3-3x+1
d(tan(√(,x)))/d(x)	sec^2(√(,x))/(2√(,x))	Find the Derivative - d/dx tan( square root of x)
d(arcsec(x))/d(x)	1/(abs(x)√(,x^2-1))	Find the Derivative
(d(tan(x))*sec(x))/d(x)	sec(x)*(tan^2(x)+sec^2(x))	Find the Derivative - d/dx tan(x)sec(x)
d()/d(x)*(25−x^2)	−2*x	Find the Derivative - d/dx 25-x^2
d()/d(x)x(3*x−9)^3	27(x−3)^2(4*x−3)	Find the Derivative - d/dx x(3x-9)^3
d(ln(cos(h(x))))/d(x)	−tan(h(x))*h(x)^′	Find the Derivative - d/dx natural log of cos(h(x))
d()/d(x)*(8/x−2/(x^3)+1/(x^4))	−8/(x^2)+6/(x^4)−4/(x^5)	Find the Derivative - d/dx 8/x-2/(x^3)+1/(x^4)
d(ln(x−1))/d(x)	1/(x−1)	Find the Derivative - d/dx natural log of x-1
d(ln(x*y))/d(x)	1/x+1/yd(y)/d(x)	Find the Derivative - d/dx natural log of xy
d()/d(x)(6x−x^2)	6 - 2x	Find the Derivative - d/dx 6x-x^2
d()/d(x)xcos(2*x)	cos(2x)−2xsin(2x)	Find the Derivative - d/dx xcos(2x)
d(arctan(cos(x)))/d(x)	−sin(x)/(1+cos^2(x))	Find the Derivative - d/dx arctan(cos(x))
d()/d(x)1/(x^11)	−11/(x^12)	Find the Derivative - d/dx 1/(x^11)
d()/d(x)4e^(−x)	−4*e^(−x)	Find the Derivative - d/dx 4e^(-x)
d()/d(x)*0	0	Find the Derivative - d/dx f(x)=0
d(4^x)/d(x)	4^x*ln(4)	Find the Derivative - d/dx f(x)=4^x
d(e^(4*x))/d(x)	4e^(4x)	Find the Derivative - d/dx f(x)=e^(4x)
d(e^(1/x))/d(x)	−(e^(1/x))/(x^2)	Find the Derivative - d/dx f(x)=e^(1/x)
d()/d(x)sin(x)/cos(x)	sec^2(x)	Find the Derivative - d/dx f(x)=(sin(x))/(cos(x))
d()/d(x)*(x^2+5)	2*x	Find the Derivative - d/d@VAR f(x)=x^2+5
d()/d(x)*x^12	12*x^11	Find the Derivative - d/d@VAR f(x)=x^12
d()/d(x)(x^2−2x)	2*x−2	Find the Derivative - d/d@VAR f(x)=x^2-2x
d()/d(x)*(x^2−1)	2*x	Find the Derivative - d/d@VAR f(x)=x^2-1
d()/d(x)*(4−x^2)	−2*x	Find the Derivative - d/d@VAR f(x)=4-x^2
12x^2−18x−12	6(2x + 1)(x - 2)	Factor 12x^2-18x-12
t^2+8	(t+2i√(,2))(t−2*i√(,2))	Factor t^2+8
(∫_^)(cos(3x)d(x))	1/3sin(3x)+C	Find the Integral cos(3x)
2*x^2−y^2=5	(2*x)/y	Find dy/dx 2x^2-y^2=5
xy^2−x^3y=6	(3x^2y−y^2)/(2xy−x^3)	Find dy/dx xy^2-x^3y=6
x^3−3x^2y+2xy^2=12	(6xy−3x^2−2y^2)/(4xy−3*x^2)	Find dy/dx x^3-3x^2y+2xy^2=12
24x^3y^2−8*y^3=−11	(3x^2y)/(y−2*x^3)	Find dy/dx 24x^3y^2-8y^3=-11
tan(4x+y)=4x	−4sin^2(4x+y)	Find dy/dx tan(4x+y)=4x
xy+2x+3*y=1	−(y+2)/(x+3)	Find dy/dx xy+2x+3y=1
x^2y^2−2x=3	(1−xy^2)/(x^2y)	Find dy/dx x^2y^2-2x=3
d()/d(x)x^9e^x	x^8e^x(x+9)	Find the Derivative - d/dx y=x^9e^x
(lim_x→−4)((1/4+1/x)/(4+x))	−1/16	Evaluate the Limit
d()/d(x)*(x^2−6)	2*x	Find the Derivative - d/dx x^2-6
2x^3−3y^2=8	(x^2)/y	Find dy/dx 2x^3-3y^2=8
(x+2)^2+(y−3)^2=37	−(x+2)/(y−3)	Find dy/dx (x+2)^2+(y-3)^2=37
sin(x+y)=y^2*cos(x)	(y^2sin(x)+cos(x+y))/(2y*cos(x)−cos(x+y))	Find dy/dx sin(x+y)=y^2cos(x)
(lim_x→0)(((2+x)^3−8)/x)	12	Evaluate the Limit limit as x approaches 0 of ((2+x)^3-8)/x
d()/d(x)(10x^5−8x+6e^x−10)	50x^4−8+6e^x	Find the Derivative - d/dx 10x^5-8x+6e^x-10
y√(,x+1)=4	−2/√(,(x+1)^3)	Find dy/dx y square root of x+1=4
ycos(x)=3x^2+4*y^2	(6x+ysin(x))/(cos(x)−8*y)	Find dy/dx ycos(x)=3x^2+4y^2
ycos(x)=4x^2+5*y^2	(8x+ysin(x))/(cos(x)−10*y)	Find dy/dx ycos(x)=4x^2+5y^2
d()/d(x)*(−csc(x)−cos(x))	csc(x)*cot(x)+sin(x)	Find the Derivative - d/dx y=-csc(x)-cos(x)
d(ln(10))/d(x)	0	Find the Derivative - d/dx natural log of 10
(d(x)*e^(−x^2))/d(x)	e^(−x^2)(1−2x^2)	Find the Derivative - d/dx xe^(-x^2)
d()/d(x)4x^(−3/8)	−3/2*x^(−11/8)	Find the Derivative - d/dx 4x^(-3/8)
d()/d(x)*(2^5⋅0)	0	Find the Derivative - d/dx 2^5*0
y=sin(x+y)	cos(x+y)/(1−cos(x+y))	Find dy/dx y=sin(x+y)
y*cos(x)=x^2+y^2	(2x+ysin(x))/(cos(x)−2*y)	Find dy/dx ycos(x)=x^2+y^2
(lim_x→−10)((x^2−100)/(x+10))	−20	Evaluate the Limit
d()/d(x)x^2e^x	x^2e^x+2x*e^x	Find dy/dx y=x^2e^x
d()/d(x)(2x^2+3*x)	4*x+3	Find the Derivative - d/dx 2x^2+3x
d()/d(x)(7x+1)^2	98*x+14	Find the Derivative - d/dx (7x+1)^2
d()/d(x)(−1/3(x^(−3)−x^6))	x^(−4)+2*x^5	Find the Derivative - d/dx -1/3(x^-3-x^6)
(d(5)xe^x)/d(x)	5e^x(x+1)	Find the Derivative - d/dx 5xe^x
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 y=(x^2-1)/(x^2+x+1)
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()/d(x)x^10e^x	x^9e^x(x+10)	Find the Derivative - d/dx y=x^10e^x
d(cos(6*x))/d(x)	−6sin(6x)	Find the Derivative - d/dx cos(6x)
ƒ(x)=x*sin(x)	2cos(x)−xsin(x)	Find the 2nd Derivative f(x)=xsin(x)
d^2()/(d(x)^2)3e^(−x^2)	6e^(−x^2)(2*x^2−1)	Find the 2nd Derivative 3e^(-x^2)
(∑_i=1^5)(2/3)	10/3	Evaluate the Summation sum from i=1 to 5 of (2/3)^(i+1)
(∑_i=1^6)(3*i+2)	75	Evaluate the Summation sum from i=1 to 6 of 3i+2
(∑_n=1^7)(2)*(−2)^(n−1)	86	Evaluate the Summation sum from n=1 to 7 of 2(-2)^(n-1)
(lim_x→0^+)(sin(x))*ln(x)	0	Evaluate Using L'Hospital's Rule
(lim_x→8)(x^3)*e^(−x^2)	512*e^(−64)	Evaluate Using L'Hospital's Rule limit as x approaches 8 of x^3e^(-x^2)
(∫_^)((e^tan(x))/cos^2(x)*d(x))	e^tan(x)+C	Evaluate the Integral
(∫_^)((e^u)/((1−e^u)^2)*d(u))	1/(1−e^u)+C	Evaluate the Integral
(∫_^)(((ln(x))^4)/x*d(x))	((ln(x))^5)/5+C	Evaluate the Integral
(∫_^)(((ln(x))^5)/x*d(x))	((ln(x))^6)/6+C	Evaluate the Integral
(∫_^)(((ln(x))^3)/x*d(x))	((ln(x))^4)/4+C	Evaluate the Integral
(∫_^)(√(,t^6+5t)(6t^5+5)d(t))	2/3(t^6+5t)^(3/2)+C	Evaluate the Integral
(∫_^)(1/√(,x^3)+5e^(5x)*d(x))	−2/√(,x)+e^(5*x)+C	Evaluate the Integral
(∫_^)(5x−7d(x))	(5x^2)/2−7x+C	Evaluate the Integral integral of 5x-7 with respect to x
(∫_^)(3x−7d(x))	(3x^2)/2−7x+C	Evaluate the Integral integral of 3x-7 with respect to x
(∫_^)(9x^2+2x−3*d(x))	3x^3+x^2−3x+C	Evaluate the Integral integral of 9x^2+2x-3 with respect to x
(∫_^)(8x^3−9x^2+4*d(x))	2x^4−3x^3+4*x+C	Evaluate the Integral
(∫_^)(1−csc(x)cot(x)d(x))	x+csc(x)+C	Evaluate the Integral
(∫_^)(2x−3d(x))	x^2−3*x+C	Evaluate the Integral integral of 2x-3 with respect to x
(∫_^)((2+2x)e^(4x+2x^2)*d(x))	1/2e^(4x+2*x^2)+C	Evaluate the Integral
(∫_^)(3x^5−8x^3+2*d(x))	1/2x^6−2x^4+2*x+C	Evaluate the Integral
d^2(tan(x))/(d(x)^2)	2sec^2(x)tan(x)	Find the 2nd Derivative y=tan(x)
e^(−∞)	0	Simplify e^negative infinity
x^(2/3)+y^(2/3)=4	−√(3,y/x)	Find dy/dx x^(2/3)+y^(2/3)=4
(∫_^)(1/(5x+4)d(x))	1/5ln(abs(5x+4))+C	Evaluate the Integral
(∫_^)(1/(5x^3)d(x))	−1/(10*x^2)+C	Evaluate the Integral integral of 1/(5x^3) with respect to x
(∫_^)(1/(3x^2)d(x))	−1/(3*x)+C	Evaluate the Integral integral of 1/(3x^2) with respect to x
(∫_^)(1/(3x^5)d(x))	−1/(12*x^4)+C	Evaluate the Integral integral of 1/(3x^5) with respect to x
(∫_^)(1/(xln(x^4))d(x))	1/4*ln(abs(ln(x)))+C	Evaluate the Integral
(∫_^)(1/(1−sin(x))*d(x))	tan(x)+sec(x)+C	Evaluate the Integral
(∫_^)(1/(1+4x^2)d(x))	1/2arctan(2x)+C	Evaluate the Integral integral of 1/(1+4x^2) with respect to x
(∫_^)(1/(x^7)*d(x))	−1/(6*x^6)+C	Evaluate the Integral integral of 1/(x^7) with respect to x
(∫_^)(1/√(,x^2−9)*d(x))	ln(abs(x+√(,x^2-9)))+C	Evaluate the Integral
(∫_^)(√(,x^2−4)/x*d(x))	√(,x^2−4)−2*arcsec(x/2)+C	Evaluate the Integral
(∫_^)((x^2+2x−3)/(x^4)d(x))	−1/x−1/(x^2)+1/(x^3)+C	Evaluate the Integral
(∫_^)((5−x)/(2x^2+x−1)d(x))	ln(abs(2x-1))-3/2ln(abs(x+1))+C	Evaluate the Integral
(∫_^)(a^x*d(x))	(a^x)/ln(a)+C	Evaluate the Integral integral of a^x with respect to x
(∫_^)(arcsin(x)/√(,1−x^2)*d(x))	((arcsin(x))^2)/2+C	Evaluate the Integral
(∫_^)((2x)/(x^2+1)d(x))	ln(x^2+1)+C	Evaluate the Integral
(∫_^)(sin^2(3x)d(x))	x/2−sin(6*x)/12+C	Evaluate the Integral integral of sin(3x)^2 with respect to x
(∫_^)(sec^3(x)tan^3(x)d(x))	sec^5(x)/5−sec^3(x)/3+C	Evaluate the Integral
(∫_^)(sin(1/x)/(x^2)*d(x))	cos(1/x)+C	Evaluate the Integral
(∫_^)(√(,1−4y)d(y))	−1/6(1−4y)^(3/2)+C	Evaluate the Integral
(∫_^)(√(,x^9)*d(x))	2/11*x^(11/2)+C	Evaluate the Integral
(∫_^)(sin(x)cos(x)d(x))	cos(x)/7−cos(x)/5+C	Evaluate the Integral
(∫_^)(e^(11x)d(x))	(e^(11*x))/11+C	Evaluate the Integral integral of e^(11x) with respect to x
(∫_^)(e^xcos(e^x)d(x))	sin(e^x)+C	Evaluate the Integral
(∫_^)(e^(−x)cos(2x)*d(x))	(e^(−x)(2sin(2x)−cos(2x)))/5+C	Evaluate the Integral
(∫_^)(e^(3x)cos(2x)d(x))	(e^(3x))/13(3cos(2x)+2sin(2x))+C	Evaluate the Integral
(∫_^)(x^11*d(x))	(x^12)/12+C	Evaluate the Integral integral of x^11 with respect to x
(∫_^)(x/(x^2+2x+2)d(x))	1/2ln(x^2+2x+2)−arctan(x+1)+C	Evaluate the Integral
(∫_^)(x/(x^2+4)*d(x))	1/2*ln(x^2+4)+C	Evaluate the Integral integral of x/(x^2+4) with respect to x
(∫_^)(x^2(x^3+5)^9d(x))	((x^3+5)^10)/30+C	Evaluate the Integral
(∫_^)(x^2e^(5x)*d(x))	see full solution →	Evaluate the Integral integral of x^2e^(5x) 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
(∫_^)(x^2sec^2(x^3)d(x))	tan(x^3)/3+C	Evaluate the Integral
(∫_^)(√(4,x^3)*d(x))	4/7*x^7/4+C	Evaluate the Integral
(∫_^)(√(3,x^8)*d(x))	(3*x^(11/3))/11+C	Evaluate the Integral
(∫_^)(√(5,x^2)*d(x))	(5*x^(7/5))/7+C	Evaluate the Integral
(∫_^)(√(5,x)*d(x))	5/6*x^(6/5)+C	Evaluate the Integral
(∫_^)(x^2sin(3x)*d(x))	see full solution →	Evaluate the Integral integral of x^2sin(3x) with respect to x
(∫_^)(x^9e^(x^10)d(x))	(e^(x^10))/10+C	Evaluate the Integral
(∫_^)(y^2√(,y)*d(y))	2/7*y^(7/2)+C	Evaluate the Integral
(∫_-3^4)(x*d(x))	7/2	Evaluate the Integral
(∫_^)(3td(t))	3/2*t^2+C	Evaluate the Integral integral of 3t with respect to t
(∫_^)(30x^(3/2)d(x))	12*x^(5/2)+C	Evaluate the Integral integral of 30x^(3/2) with respect to x
(∫_−4^2)(2x+4d(x))	12	Evaluate the Integral
(∫_−4^4)(16−x^2*d(x))	256/3	Evaluate the Integral
(∫_^)(2cos(2x)*d(x))	sin(2*x)+C	Evaluate the Integral integral of 2cos(2x) with respect to x
(∫_7^2)(g(x)*d(x))	−(∫_2^7)(g(x)*d(x))	Evaluate the Integral
(∫_^)(6x−5d(x))	3x^2−5x+C	Evaluate the Integral integral of 6x-5 with respect to x
(∫_^)(6*d(k))	6*k+C	Evaluate the Integral integral of 6 with respect to k
(∫_^)(6e^(−7x)*d(x))	−6/7e^(−7x)+C	Evaluate the Integral integral of 6e^(-7x) with respect to x
(∫_^)(6x^(1/2)d(x))	4*x^(3/2)+C	Evaluate the Integral integral of 6x^(1/2) with respect to x
(∫_^)(8e^(4x)*d(x))	2e^(4x)+C	Evaluate the Integral integral of 8e^(4x) with respect to x
(∫_^)(5x^(−1)d(x))	5*ln(abs(x))+C	Evaluate the Integral
(∫_^)(4e^(2x)*d(x))	2e^(2x)+C	Evaluate the Integral integral of 4e^(2x) with respect to x
(∫_^)(4e^(4x)*d(x))	e^(4*x)+C	Evaluate the Integral integral of 4e^(4x) with respect to x
(∫_^)(5(t^2−5t−2)*d(t))	(5t^3)/3−(25t^2)/2−10*t+C	Evaluate the Integral
d()/d(I)*ln(∞)	0	Find the Derivative - d/dI natural log of infinity
d()/d(x)*4	0	Find the Derivative - d/dx 4
(∫_^)(ln(4x)d(x))	xln(4x)−x+C	Evaluate the Integral
(∫_^)(ln(7x)d(x))	xln(7x)−x+C	Evaluate the Integral
(∫_^)(sin(4x)cos(4x)d(x))	−1/16cos(8x)+C	Evaluate the Integral
(∫_^)(sin(y)*d(y))	−cos(y)+C	Evaluate the Integral integral of sin(y) with respect to y
(∫_^)(sec(4x)d(x))	1/4ln(abs(sec(4x)+tan(4*x)))+C	Evaluate the Integral
(∫_^)(sec(3x)d(x))	1/3ln(abs(sec(3x)+tan(3*x)))+C	Evaluate the Integral
(∫_^)(sec(x)(sec(x)+tan(x))d(x))	tan(x)+sec(x)+C	Evaluate the Integral
(∫_^)(xln(2x)*d(x))	(x^2ln(2x))/2−(x^2)/4+C	Evaluate the Integral
(∫_^)(x(x^2−1)^4d(x))	((x^2−1)^5)/10+C	Evaluate the Integral integral of x(x^2-1)^4 with respect to x
(∫_^)(xtan^2(x)d(x))	x*tan(x)+ln(abs(cos(x)))-(x^2)/2+C	Evaluate the Integral
(∫_0^1)(e^(−x)*d(x))	1−1/e	Evaluate the Integral
(∫_0^1)(√(,1−x^2)*d(x))	π/4	Evaluate the Integral
(∫_0^1)((u+2)(u−3)d(u))	−37/6	Evaluate the Integral
(∫_0^11)(√(,121−x^2)*d(x))	(121*π)/4	Evaluate the Integral
(∫_0^6)(x/√(,9+2x^2)d(x))	3	Evaluate the Integral
(∫_0^2)(8x^2d(x))	64/3	Evaluate the Integral
(∫_1^2)((2u^2+3)d(u))	23/3	Evaluate the Integral
(∫_1^2)((t+1/t)^2*d(t))	29/6	Evaluate the Integral
(∫_1^3)(x^2ln(x)d(x))	9*ln(3)−26/9	Evaluate the Integral
(∫_1^3)(1/x*d(x))	ln(3)	Evaluate the Integral
(∫_1^3)(x^2*d(x))	26/3	Evaluate the Integral
(∫_2^3)(1/√(,x)−7*d(x))	2√(,3)−2√(,2)−7	Evaluate the Integral
(∫_−2^2)(x*d(x))	0	Evaluate the Integral
(∫_−2^3)(36−x^2*d(x))	505/3	Evaluate the Integral
(∫_^)(15x^(1/2)d(x))	10*x^(3/2)+C	Evaluate the Integral integral of 15x^(1/2) with respect to x
(∫_^)(15x^(3/2)d(x))	6*x^(5/2)+C	Evaluate the Integral integral of 15x^(3/2) with respect to x
(∫_^)(16xd(x))	8*x^2+C	Evaluate the Integral integral of 16x with respect to x
(∫_^)(11x^(−6)d(x))	−11/(5*x^5)+C	Evaluate the Integral integral of 11x^-6 with respect to x
(∫_10^13)(2xd(x))	69	Evaluate the Integral
(∫_1^8)(1/x*d(x))	ln(8)	Evaluate the Integral
(∫_1^8)(ln(x)/x*d(x))	((ln(8))^2)/2	Evaluate the Integral
(∫_1^6)(x√(,5x^2+4)d(x))	(368√(,46)−27)/15	Evaluate the Integral
(8/27)^(−1/3)*(81/256)^(−1/4)	2	Evaluate (8/27)^(-1/3)(81/256)^(-1/4)
d()/d(x)(∫_^)(√(,x)d(x))	√(,x)	Find the Derivative of the Integral
d()/d(x)1/3*x^3	x^2	Find the Derivative - d/dx 1/3x^3
d()/d(x)(∫_^)(tan(x)d(x))	tan(x)	Find the Derivative of the Integral integral of tan(x) with respect to x
d()/d(x)(∫_^)(xcos(x)*d(x))	x*cos(x)	Find the Derivative of the Integral integral of xcos(x) with respect to x
d()/d(x)(3x^2−4*x)	6*x−4	Find the Derivative - d/dx 3x^2-4x
d^3()/(d(x)^3)1/x	−6/(x^4)	Find the 3rd Derivative y=1/x
d()/d(x)*(x/12−12/x)	1/12+12/(x^2)	Find the Derivative - d/dx x/12-12/x
(x^2+y^2)^2=4x^2y	(2xy−x^3−xy^2)/(yx^2+y^3−x^2)	Find dy/dx (x^2+y^2)^2=4x^2y
d()/d(x)*e^(−x)√(,x)	(e^(−x)(1−2x))/(2√(,x))	Find the Derivative - d/d@VAR f(x)=e^(-x) square root of x
(∫_1^2)((e^(1/x))/(x^2)*d(x))	e−√(,e)	Evaluate the Integral
Average Value of d(25−x^2)/d(x)* on *[−5,5]	0	Find the Average Value of the Derivative y=25-x^2 , [-5,5]
ƒ(x)=1/2x^4+2x^3	see full solution →	Find the Concavity f(x)=1/2x^4+2x^3
y=x^3−6x^2−36x	(2,−88)	Find the Inflection Points y=x^3-6x^2-36x
ƒ(x)=x+1/x	1, -1	Find the Critical Points x+1/x
ƒ(x)=x^3+3x^2−24x+6	see full solution →	Find Where Increasing/Decreasing Using Derivatives f(x)=x^3+3x^2-24x+6
ƒ(x)=2x^3+3x^2−72*x	see full solution →	Find Where Increasing/Decreasing Using Derivatives f(x)=2x^3+3x^2-72x
x^2+y^2=−14*x	7, y = -7	Find the Horizontal Tangent Line x^2+y^2=-14x
sin(3)	sin(3)≈0.14112	Evaluate sin(3)
arcsin(0)	0	Evaluate arcsin(0)
cos(5*π)	−1	Evaluate cos(5pi)
arctan(1/2)	arctan(1/2)≈0.4636* rad	Evaluate arctan(1/2)
ƒ(x)=3x^2−12x−8	2	Find the Critical Points f(x)=3x^2-12x-8
x^3−3*x	1, -1	Find the Critical Points x^3-3x
ƒ(x)=(2x^2+3)/(4x^2+5)	0	Find the Critical Points f(x)=(2x^2+3)/(4x^2+5)
ƒ(x)=x/(x^2+4)	−2,2	Find the Critical Points f(x)=x/(x^2+4)
ƒ(x)=2x^3+3x^2−12*x	−2,1	Find the Critical Points f(x)=2x^3+3x^2-12x
ƒ(x)=x^4−6*x^2	0,√(,3),−√(,3)	Find the Critical Points f(x)=x^4-6x^2
ƒ(x)=13x^4−78x^2	0,√(,3),−√(,3)	Find the Critical Points f(x)=13x^4-78x^2
7^(1/4)⋅49^(−5/8)	1/7	Evaluate 7^(1/4)*49^(-5/8)
sec(π/6)	4/3	Evaluate sec(pi/6)^2
2*e^0	2	Evaluate 2e^0
d()/d(x)(3x+7)^2	6(3x+7)	Find the Derivative - d/dx (3x+7)^2
ƒ(x)=(x^2+1)/(x^2−1)	1,x=−1; Horizontal Asymptote: *y=1	Find the Asymptotes f(x)=(x^2+1)/(x^2-1)
d()/d(x)1/((x+3)^2)	−2/((x+3)^3)	Find the Derivative - d/dx 1/((x+3)^2)
d()/d(x)*(2^6⋅0)	0	Find the Derivative - d/dx 2^6*0
d()/d(x)*(x/10−10/x)	1/10+10/(x^2)	Find the Derivative - d/dx x/10-10/x
d()/d(x)*(x/11−11/x)	1/11+11/(x^2)	Find the Derivative - d/dx x/11-11/x
d(√(,x*e^x))/d(x)	(e^x(1+x))/(2√(,xe^x))	Find the Derivative - d/dx square root of xe^x
(d(6)*x^4)/d(x)	24*x^3	Find the Derivative - d/dx 6x^4
(lim_x→100)((√(,x)−10)/(x−100))	1/20	Evaluate the Limit
d(tan(x))/d(x)	sec^2(x)	Find dy/dx y=tan(x)
d(y)/d(x)* for *y=x^3	3*x^2	Find dy/dx y=x^3
xy=cot(xy)	−y/x	Find dy/dx xy=cot(xy)
d()/d(x)(1/4x^2−1/2*ln(x))	1/2x−1/(2x)	Find the Derivative - d/dx 1/4x^2-1/2 natural log of x
d()/d(x)(10x^3+7)^(3/2)	45x^2√(,10x^3+7)	Find dy/dx y=(10x^3+7)^(3/2)
d()/d(x)(5x^2+11*x)^20	20(10x+11)(5x^2+11*x)^19	Find dy/dx y=(5x^2+11x)^20
d()/d(x)*7^x	7^x*ln(7)	Find dy/dx y=7^x
(y−3)^2=4*(x−5)	2/(y−3)	Find dy/dx (y-3)^2=4(x-5)
e^ycos(x)=6+sin(xy)	(ycos(xy)+e^ysin(x))/(e^ycos(x)−xcos(xy))	Find dy/dx e^ycos(x)=6+sin(xy)
x^2+y^2=2xy	1	Find dy/dx x^2+y^2=2xy
x^3+y^3=8	−(x^2)/(y^2)	Find dy/dx x^3+y^3=8
x^3+y^3=9	−(x^2)/(y^2)	Find dy/dx x^3+y^3=9
y^2−x^3=22	(3x^2)/(2y)	Find dy/dx y^2-x^3=22
y^2=(x^2)/(x*y−2500)	(2x−y^3)/(3xy^2−5000y)	Find dy/dx y^2=(x^2)/(xy-2500)
2*x^2+y^2=66	−(2*x)/y	Find dy/dx 2x^2+y^2=66
3xy−x^2−4=0	(2x−3y)/(3*x)	Find dy/dx 3xy-x^2-4=0
5y^2=(4x−3)/(4*x+3)	12/(5y(4*x+3)^2)	Find dy/dx 5y^2=(4x-3)/(4x+3)
d()/d(A)(180A−0.30*A^3)	180−0.9*A^2	Find ds/dA s=180A-0.30A^3
x+y=x*y	(y−1)/(1−x)	Find dy/dx x+y=xy
tan(x/y)=x+y	(ysec^2(x/y)−y^2)/(y^2+xsec^2(x/y))	Find dy/dx tan(x/y)=x+y
sin(x+y)=x*y	(y−cos(x+y))/(cos(x+y)−x)	Find dy/dx sin(x+y)=xy
sin(x*y)=y	(ycos(xy))/(1−xcos(xy))	Find dy/dx sin(xy)=y
x^4+y^4=16	−(x^3)/(y^3)	Find dy/dx x^4+y^4=16
x^3+x^2y+4y^2=6	−(3x^2+2xy)/(x^2+8y)	Find dy/dx x^3+x^2y+4y^2=6
x^2−y^2=16	x/y	Find dy/dx x^2-y^2=16
x^2+y^2=5	−x/y	Find dy/dx x^2+y^2=5
x^2+4*y^2=36	−x/(4*y)	Find dy/dx x^2+4y^2=36
arccos(1)	0	Evaluate arccos(1)
x^(2/3)+y^(2/3)=5	−√(3,y/x)	Find dy/dx x^(2/3)+y^(2/3)=5
(x^2−4*x)/(x+5)>0	(x^2−4*x)/(x+5)>0⇒(−5,0)∪(4,∞)	Convert to Interval Notation (x^2-4x)/(x+5)>0
(∫_^)(2e^xd(x))	2*e^x+C	Find the Integral 2e^x
(∫_^)(y^2*d(y))	(y^3)/3+C	Find the Integral y^2
(∫_^)(2xd(x))	x^2+C	Find the Integral 2x
a^2−2*a−1	(a−1−√(,2))*(a−1+√(,2))	Factor a^2-2a-1
x^3−12*x	x*(x^2−12)	Factor x^3-12x
−3x^2+8x+16	(3x+4)(4−x)	Factor -3x^2+8x+16
36x^2−54x−36	18(2x + 1)(x - 2)	Factor 36x^2-54x-36
d()/d(x)x/(x^2+1)	(1−x^2)/((x^2+1)^2)	Find the Derivative - d/d@VAR f(x)=x/(x^2+1)
d()/d(x)8/(x^2)	−16/(x^3)	Find the Derivative - d/d@VAR f(x)=8/(x^2)
d()/d(x)5/(x^2)	−10/(x^3)	Find the Derivative - d/d@VAR f(x)=5/(x^2)
d()/d(x)√(,1−6*x)	(−3)/√(,1−6*x)	Find the Derivative - d/d@VAR f(x) = square root of 1-6x
d()/d(x)(ax+b)/(cx+d)	(ad−bc)/((c*x+d)^2)	Find the Derivative - d/d@VAR f(x)=(ax+b)/(cx+d)
d()/d(x)ln(x)/(x^2)	(1−2*ln(x))/(x^3)	Find the Derivative - d/d@VAR f(x)=( natural log of x)/(x^2)
d()/d(x)*(x^2+x−7)	2*x+1	Find the Derivative - d/d@VAR f(x)=x^2+x-7
d()/d(x)*(2^4⋅0)	0	Find the Derivative - d/d@VAR f(x)=2^4*0
d()/d(x)*(x^2−4)	2*x	Find the Derivative - d/d@VAR f(x)=x^2-4
d(5^x)/d(x)	5^x*ln(5)	Find the Derivative - d/d@VAR f(x)=5^x
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/d@VAR f(x)=(3x-8) natural log of 2x^5+3
d()/d(x)(7x−3)	7	Find the Derivative - d/d@VAR f(x)=7x-3
d()/d(x)(x^2)/(x−1)	(x^2−2*x)/((x−1)^2)	Find the Derivative - d/d@VAR f(x)=(x^2)/(x-1)
(∫_^)(sin(2x)d(x))	−1/2cos(2x)+C	Find the Antiderivative sin(2x)
d(√(3,x^2))/d(x)	2/(3√(3,x))	Find the Derivative - d/dx f(x) = cube root of x^2
d()/d(x)√(,2)	0	Find the Derivative - d/dx f(x) = square root of 2
d(p^3)/d(x)	0	Find the Derivative - d/dx f(x)=p^3
d(9^x)/d(x)	9^x*ln(9)	Find the Derivative - d/dx f(x)=9^x
d()/d(x)(ax+b)/(cx+d)	(ad−bc)/((c*x+d)^2)	Find the Derivative - d/dx f(x)=(ax+b)/(cx+d)
d(e^(5*x))/d(x)	5e^(5x)	Find the Derivative - d/dx f(x)=e^(5x)
d((log_4)(x))/d(x)	1/(x*ln(4))	Find the Derivative - d/dx log base 4 of x
d(3^x)/d(x)	3^x*ln(3)	Find the Derivative - d/dx f(x)=3^x
(∫_^)(8*d(x))	8*x+C	Evaluate the Integral integral of 8 with respect to x
(d(5)*x^2)/d(x)	10*x	Find the Derivative - d/dx f(x)=5x^2
d()/d(x)4x	4	Find the Derivative - d/dx f(x)=4x
d()/d(x)(3x+1)^(x−3)	(3x+1)^(x−3)(ln(3x+1)+(3x−9)/(3*x+1))	Find the Derivative - d/dx y=(3x+1)^(x-3)
d()/d(x)(3x^4*ln(x))	3x^3(1+4*ln(x))	Find the Derivative - d/dx f(x)=3x^4 natural log of x
d(arctan(1/x))/d(x)	−1/(x^2+1)	Find the Derivative - d/dx arctan(1/x)
d(cos(arcsin(x)))/d(x)	−x/√(,1−x^2)	Find the Derivative - d/dx cos(arcsin(x))
d(arcsec(2*x))/d(x)	1/(abs(x)√(,4*x^2-1))	Find the Derivative
(d(−)3x^2)/d(x)	−6*x	Find the Derivative - d/dx -3x^2
d()/d(x)(x^2−2x+3)	2*x−2	Find the Derivative - d/dx x^2-2x+3
d(x^(e^x))/d(x)	x^(e^x)e^x(ln(x)+1/x)	Find the Derivative - d/dx x^(e^x)
d(x^(5/2))/d(x)	5/2*x^(3/2)	Find the Derivative - d/dx x^(5/2)
(d(6)*cos(x))/d(x)	−6*sin(x)	Find the Derivative - d/dx 6cos(x)
d()/d(x)1/(x^4)	−4/(x^5)	Find the Derivative - d/dx f(x)=1/(x^4)
d()/d(t)(3t^2−30*t+72)	6*t−30	Find the Derivative - d/dt 3t^2-30t+72
d(x)/d(x)	1	Find the Derivative
d((log_)(3*x))/d(x)	1/(x*ln(10))	Find the Derivative - d/dx log of 3x
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(ln(ln(6*x)))/d(x)	1/(xln(6x))	Find the Derivative - d/dx natural log of natural log of 6x
d(ln(cos(2*x)))/d(x)	−2tan(2x)	Find the Derivative - d/dx natural log of cos(2x)
d(sin(x))/d(x)	see full solution →	Find the Derivative - d/dx (sin(x))^( natural log of x)
d(sin(tan(x)))/d(x)	cos(tan(x))*sec^2(x)	Find the Derivative - d/dx sin(tan(x))
d()/d(x)(x/3.3+3.3/x)(x^2+1)	(x^2)/1.1+11.89/3.3−3.3/(x^2)	Find the Derivative - d/dx (x/3.3+3.3/x)(x^2+1)
d()/d(x)*(x/3−3/x)	1/3+3/(x^2)	Find the Derivative - d/dx y=x/3-3/x
d()/d(x)(x−3x^(1/3))	1−x^(−2/3)	Find the Derivative - d/dx x-3x^(1/3)
d()/d(x)9x^4	36*x^3	Find the Derivative - d/dx 9x^4
y=√(,x−9)/√(,x+9)	9/(√(,x−9)*(x+9)^(3/2))	Find dy/dx
(d(sec(x))*tan(x))/d(x)	sec^3(x)+sec(x)*tan^2(x)	Find the Derivative - d/dx f(x)=sec(x)tan(x)
d(arctan(x))/d(x)	1/(1+x^2)	Find the Derivative - d/dx f(x)=arctan(x)
d()/d(x)8x	8	Find the Derivative - d/dx f(x)=8x
d(ln(√(5,x)))/d(x)	1/(5*x)	Find the Derivative - d/dx natural log of fifth root of x
d()/d(x)2(4−7*x)^4	−56(4−7x)^3	Find the Derivative - d/dx g(x)=2(4-7x)^4
d()/d(x)(x−2)(2*x+3)	4*x−1	Find the Derivative - d/dx h(x)=(x-2)(2x+3)
d(cos(x))/d(x)	−8cos(x)sin(x)	Find the Derivative - d/dx cos(x)^8
d()/d(x)(x+3)^2e^(4*x)	2(x+3)(2x+7)e^(4*x)	Find the Derivative - d/dx y=(x+3)^2e^(4x)
d()/d(x)5/x	−5/(x^2)	Find the Derivative - d/dx y=5/x
d()/d(x)4/x	−4/(x^2)	Find the Derivative - d/dx y=4/x
d()/d(x)*19^x	19^x*ln(19)	Find the Derivative - d/dx y=19^x
d()/d(x)(x^3)/3	x^2	Find the Derivative - d/dx y=(x^3)/3
d()/d(x)√(,1+8*x)	4/√(,1+8*x)	Find the Derivative - d/dx y = square root of 1+8x
d()/d(x)√(,5−9*x)	−9/(2√(,5−9*x))	Find the Derivative - d/dx y = square root of 5-9x
d()/d(x)√(3,2*x)	2/(3√(3,4*x^2))	Find the Derivative - d/dx y = cube root of 2x
d(sec(x))/d(x)	4sec(x)tan(x)	Find the Derivative - d/dx sec(x)^4
d()/d(x)*(x/6−6/x)	1/6+6/(x^2)	Find the Derivative - d/dx y=x/6-6/x
(d(5)*cos(x))/d(x)	−5*sin(x)	Find the Derivative - d/dx 5cos(x)
d()/d(x)*(−x/y)	(x*y^′−y)/(y^2)	Find the Derivative - d/dx -x/y
d()/d(x)*x^(4/9)	4/9*x^(−5/9)	Find the Derivative - d/dx y=x^(4/9)
d()/d(x)*(x^(5/3)−x^(2/3))	5/3x^(2/3)−2/3x^(−1/3)	Find the Derivative - d/dx y=x^(5/3)-x^(2/3)
d()/d(x)sin(tan(9x))	9cos(tan(9x))sec^2(9x)	Find the Derivative - d/dx y=sin(tan(9x))
d()/d(x)*x^12	12*x^11	Find the Derivative - d/dx y=x^12
d()/d(x)*(x^2+4)	2*x	Find the Derivative - d/dx y=x^2+4
d()/d(x)−4*x^2	−8*x	Find the Derivative - d/dx -4x^2
d()/d(x)x^2sin(6*x)	6x^2cos(6x)+2xsin(6x)	Find the Derivative - d/dx y=x^2sin(6x)
d()/d(x)(5√(,x))/6	5/(12√(,x))	Find the Derivative - d/dx y=(5 square root of x)/6
d()/d(x)arcsin(6x+1)	6/√(,−36x^2−12x)	Find the Derivative - d/dx y=arcsin(6x+1)
d(sec^2(x))/d(x)	2sec^2(x)tan(x)	Find the Derivative - d/dx y=sec(x)^2
d()/d(x)(e^(7x^2)+x)	14xe^(7*x^2)+1	Find the Derivative - d/dx y=e^(7x^2)+x
d(e^(7*x))/d(x)	7e^(7x)	Find the Derivative - d/dx y=e^(7x)
d()/d(x)e^(−6x)	−6e^(−6x)	Find the Derivative - d/dx y=e^(-6x)
d()/d(x)ln(x)/(x^4)	(1−4*ln(x))/(x^5)	Find the Derivative - d/dx y=( natural log of x)/(x^4)
d()/d(x)((8x^3)/3−7*x)	8*x^2−7	Find the Derivative - d/dx y=(8x^3)/3-7x
d()/d(x)(5x−2)/(4x+3)	23/((4*x+3)^2)	Find the Derivative - d/dx y=(5x-2)/(4x+3)
d()/d(x)(5*x)/(1+x^2)	(5*(1−x^2))/((1+x^2)^2)	Find the Derivative - d/dx (5x)/(1+x^2)
d()/d(x)*(x^2+x^3)^4	4x^7(1+x)^3(2+3x)	Find the Derivative - d/dx y=(x^2+x^3)^4
d()/d(x)ln(x^2e^x)	(2+x)/x	Find the Derivative - d/dx y = natural log of x^2e^x
d(ln(6*x))/d(x)	1/x	Find the Derivative - d/dx y = natural log of 6x
d()/d(x)*ln(sec(x)+tan(x))	sec(x)	Find the Derivative - d/dx y = natural log of sec(x)+tan(x)
d()/d(x)ln(8−3x)	(−3)/(8−3*x)	Find the Derivative - d/dx y = natural log of 8-3x
d()/d(x)(3x+7)	3	Find the Derivative - d/dx 3x+7
d()/d(x)*ln(ln(x^2))	1/(x*ln(x))	Find the Derivative - d/dx y = natural log of natural log of x^2
d()/d(x)(4x^3+3x^2)/x	8*x+3	Find the Derivative - d/dx (4x^3+3x^2)/x
d(cos(x^3))/d(x)	−3x^2sin(x^3)	Find the Derivative - d/dx y=cos(x^3)
d()/d(x)(x^2+2x)	2*x+2	Find the Derivative - d/dx y=x^2+2x
d()/d(x)(3x^2−11*x)	6*x−11	Find the Derivative - d/dx y=3x^2-11x
d()/d(x)2sin(x)	2*cos(x)	Find the Derivative - d/dx y=2sin(x)
d()/d(x)4sin(x)*cos(x)	4cos(2x)	Find the Derivative - d/dx y=4sin(x)cos(x)
d()/d(x)(2x−5)^4*(x^2+x+1)^5	(2x−5)^3(x^2+x+1)^4(28x^2−32*x−17)	Find the Derivative - d/dx (2x-5)^4(x^2+x+1)^5
d()/d(x)2x*sin(x)	2xcos(x)+2*sin(x)	Find the Derivative - d/dx 2xsin(x)
d()/d(y)cy^(−6)	−6cy^(−7)	Find the Derivative - d/dy b(y)=cy^-6
d()/d(y)y/x	1/x	Find the Derivative - d/dy y/x
d()/d(y)3y	3	Find the Derivative - d/dy 3y
(d(3)*y^2)/d(y)	6*y	Find the Derivative - d/dy 3y^2
d()/d(x)*tan(e^x)	e^x*sec^2(e^x)	Find the Derivative - d/dx y=tan(e^x)
d()/d(x)(x−1/90x^3)	1−1/30*x^2	Find the Derivative - d/dx y=x-1/90x^3
(∫_^)(6xd(x))	3*x^2+C	Find the Integral 6x
(∫_^)(cot(x)*d(x))	ln(abs(sin(x)))+C	Evaluate the Integral
(∫_^)(sin(x)cos(x)d(x))	sin^2(x)/2+C	Find the Integral sin(x)cos(x)
(∫_^)(x√(,x)*d(x))	2/5*x^(5/2)+C	Find the Integral x square root of x
(∫_^)(x^5*d(x))	(x^6)/6+C	Find the Integral x^5
(∫_^)(xe^(2x)*d(x))	1/2xe^(2x)−1/4e^(2*x)+C	Find the Integral xe^(2x)
(∫_^)(1/(y^2)*d(y))	−1/y+C	Find the Integral 1/(y^2)
(∫_^)(2^x*d(x))	2^x/ln(2)+C	Find the Integral 2^x
(∫_^)(3/x*d(x))	3*ln(x)	Evaluate the Integral
d()/d(x)(5x)/(2x^2)	−5/(2*x^2)	Find the Derivative Using Product Rule - d/dx (5x)/(2x^2)
d()/d(x)1/(x^3)	−3/(x^4)	Find the Derivative Using Quotient Rule - d/dx 1/(x^3)
sin(√(,x))	sin(√(,x))	Simplify sin( square root of x)
(√(,x)+1/√(3,x))^2	x+2√(6,x)+1/√(3,x^2)	Simplify
d()/d(t)(2t^2+√(,t^3))	4*t+(3√(,t))/2	Find the Derivative - d/dt 2t^2+ square root of t^3
d(t^2)/d(t)	2*t	Find the Derivative - d/dt t^2
d()/d(F)*F(x)^′	0	Find the Derivative - d/dF F'(x)
d()/d(r)r/√(,r^2+1)	1/((r^2+1)^(3/2))	Find the Derivative - d/dr r/( square root of r^2+1)
d(tan(ln(a*x+b)))/d(a)	(xsec^2(ln(ax+b)))/(a*x+b)	Find the Derivative - d/da tan( natural log of ax+b)
(∫_^)(1/(x^4)*d(x))	−1/(3*x^3)+C	Evaluate the Integral integral of 1/(x^4) with respect to x
d()/d(x)(−2x^3)	−6*x^2	Find the Derivative - d/d@VAR f(x)=-2x^3
d(x-2)/d(x)	1	Find the Derivative
d()/d(x)*x^13	13*x^12	Find the Derivative - d/d@VAR f(x)=x^13
(lim_x→5)((x-5)/(x-5))	1	Find the Derivative
d()/d(x)(e^(3x^3+1)ln(2x^3+3))	3x^2e^(3x^3+1)(2/(2x^3+3)+3ln(2*x^3+3))	Find the Derivative - d/d@VAR f(x)=e^(3x^3+1) natural log of 2x^3+3
d()/d(x)12/x	−12/(x^2)	Find the Derivative - d/d@VAR f(x)=12/x
d()/d(x)(−3x^2+6*x−8)	−6*x+6	Find the Derivative - d/d@VAR f(x)=-3x^2+6x-8
d()/d(x)x^(4/5)(x−9)^2	(2(x−9)(7x−18))/(5x^(1/5))	Find the Derivative - d/dx x^(4/5)(x-9)^2
d()/d(x)10x^2	20*x	Find the Derivative - d/dx 10x^2
d(2^(x^2))/d(x)	2x⋅2^(x^2)ln(2)	Find the Derivative - d/dx 2^(x^2)
d(ln(x^(1/3)))/d(x)	1/(3*x)	Find the Derivative - d/dx natural log of (x)^(1/3)
d()/d(x)(x^3−9x)	3*x^2−9	Find the Derivative - d/dx x^3-9x
d(sin(2*x))/d(x)	2sin(4x)	Find the Derivative - d/dx sin(2x)^2
d(cot(sin(x)))/d(x)	−2cos(x)cot(sin(x))*csc^2(sin(x))	Find the Derivative - d/dx cot(sin(x))^2
(d(12)*x)/d(x)	12	Find the Derivative - d/dx 12x
d()/d(x)(x^3+8)/(x+2)	2*x−2	Find the Derivative - d/dx y=(x^3+8)/(x+2)
d()/d(x)4x*y	4xd(y)/d(x)+4y	Find the Derivative - d/dx 4xy
d(cos((1−2*x)^2))/d(x)	4(1−2x)sin((1−2x)^2)	Find the Derivative - d/dx cos((1-2x)^2)
d()/d(x)(x^2−4x−6)(x^3−5x^2−3*x)	5x^4−36x^3+33x^2+84x+18	Find the Derivative - d/dx y=(x^2-4x-6)(x^3-5x^2-3x)
d()/d(x)*(−9)	0	Find the Derivative - d/dx y=-9
(d(3)sin(2x))/d(x)	6cos(2x)	Find the Derivative - d/dx 3sin(2x)
d()/d(x)(4x^3−88x^2+484x)	12x^2−176x+484	Find the Derivative - d/dx 4x^3-88x^2+484x
d()/d(x)3x^(1/3)	x^(−2/3)	Find the Derivative - d/dx 3x^(1/3)
d()/d(x)2xln(8x+x)	2ln(9x)+2	Find the Derivative - d/dx 2x natural log of 8x+x
(d(2)cos(3x))/d(x)	−6sin(3x)	Find the Derivative - d/dx 2cos(3x)
d(sin(6*x))/d(x)	6cos(6x)	Find the Derivative - d/dx sin(6x)
d()/d(x)√(11,x)	1/(11*x^(10/11))	Find the Derivative - d/dx 11 root of x
d(√(3,ln(x)))/d(x)	1/(3*x√(3,(ln(x))^2))	Find the Derivative - d/dx cube root of natural log of x
d()/d(x)(2x^3+6*x^2−1)	6x^2+12x	Find the Derivative - d/dx y=2x^3+6x^2-1
(d(6)*x^3)/d(x)	18*x^2	Find the Derivative - d/dx 6x^3
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative - d/dx y=sec(x)
d(sin(sin(sin(x))))/d(x)	cos(sin(sin(x)))cos(sin(x))cos(x)	Find the Derivative - d/dx sin(sin(sin(x)))
d()/d(x)*(−7)	0	Find the Derivative - d/dx y=-7
d(√(,6+5*x))/d(x)	5/(2√(,6+5*x))	Find the Derivative - d/dx square root of 6+5x
d()/d(x)xsin(1/x)	see full solution →	Find the Derivative - d/dx xsin(1/x)
d()/d(x)2x^2*y	4xy+2*x^2d(y)/d(x)	Find the Derivative - d/dx 2x^2y
d(e^(2*x^2))/d(x)	4xe^(2*x^2)	Find the Derivative - d/dx e^(2x^2)
d()/d(x)ln(x)/(4*x)	(1−ln(x))/(4*x^2)	Find the Derivative - d/dx ( natural log of x)/(4x)
d(x^2−1)/d(x)	4x^3−4x	Find the Derivative - d/dx (x^2-1)^2
d(arcsin(6*x+1))/d(x)	6/√(,−36x^2−12x)	Find the Derivative - d/dx arcsin(6x+1)
d(p^x)/d(x)	p^x*ln(p)	Find the Derivative - d/dx p^x
d()/d(x)8/(x^3)	−24/(x^4)	Find the Derivative - d/dx 8/(x^3)
(d(−)*csc(x))/d(x)	2csc(x)cot(x)	Find the Derivative - d/dx -csc(x)^2
d()/d(x)(64*x)/(x^2+64)	(64*(64−x^2))/((x^2+64)^2)	Find the Derivative - d/dx (64x)/(x^2+64)
d()/d(x)*(−3)	0	Find the Derivative - d/dx y=-3
d(5*x+1)/d(x)	10(5x+1)	Find the Derivative - d/dx (5x+1)^2
d(e^(x/10))/d(x)	(e^(x/10))/10	Find the Derivative - d/dx e^(x/10)
d(e^(3*ln(x^2)))/d(x)	6*x^5	Find the Derivative - d/dx e^(3 natural log of x^2)
d()/d(x)4/√(3,x)	−4/(3*x√(3,x))	Find the Derivative - d/dx 4/( cube root of x)
d()/d(x)(x−4)^2(4*x−4)	12(x−4)(x−2)	Find the Derivative - d/dx (x-4)^2(4x-4)
d(4*x−x^2)/d(x)	6(4x−x^2)^2*(2−x)	Find the Derivative - d/dx (4x-x^2)^3
d()/d(x)[(x^2+x^3)(x+9)]	4x^3+30x^2+18*x	Find the Derivative - d/dx [(x^2+x^3)(x+9)]
(d(−)3cos(x))/d(x)	3*sin(x)	Find the Derivative - d/dx -3cos(x)
d()/d(x)(x^2+3x−4)	2*x+3	Find the Derivative - d/dx x^2+3x-4
d()/d(x)2/(3*x)	−2/(3*x^2)	Find the Derivative - d/dx 2/(3x)
d()/d(x)(2*x)/(x^2)	−2/(x^2)	Find the Derivative - d/dx (2x)/(x^2)
d()/d(x)(2*x)/(x^2+100)	(200−2*x^2)/((x^2+100)^2)	Find the Derivative - d/dx (2x)/(x^2+100)
d()/d(x)1/(2*x−3)	−2/((2*x−3)^2)	Find the Derivative - d/dx 1/(2x-3)
d(sin(tan(3*x)))/d(x)	3sec^2(3x)cos(tan(3x))	Find the Derivative - d/dx sin(tan(3x))
d()/d(x)*(x−x^7)	1−7*x^6	Find the Derivative - d/dx y=x-x^7
d()/d(x)1/(x+4)	−1/((x+4)^2)	Find the Derivative - d/dx 1/(x+4)
d()/d(x)(x^2−6*x+12)/(x−4)	(x^2−8*x+12)/((x−4)^2)	Find the Derivative - d/dx (x^2-6x+12)/(x-4)
d()/d(u)(u−√(,u))(u+√(,u))	2*u−1	Find the Derivative - d/du
d(e^(4*t))/d(t)	4e^(4t)	Find the Derivative - d/dt e^(4t)
d()/d(x)*((x+1)/(x−1))^2	(−4*(x+1))/((x−1)^3)	Find the Derivative - d/dx ((x+1)/(x-1))^2
2x^3−4x^2+x−2	(x−2)(2x^2+1)	Simplify f(x)*(2x^3)-4x^2+x-2
sec(x)*tan(x)	sin(x)/cos^2(x)	Simplify sec(x)tan(x)
x(x^(1/2))	x^(3/2)	Simplify x(x^(1/2))
b^8(2b)^4	16*b^12	Simplify b^8(2b)^4
x(20−2x)(20−2x)	4x^3−80x^2+400*x	Simplify (x)(20-2x)(20-2x)
x=√(6,x)	{0,1}	Solve for x x = sixth root of x
6x^2−144x+486=0	12±3√(,7)	Solve for x 6x^2-144x+486=0
12x^2−176x+484=0	11,11/3	Solve for x 12x^2-176x+484=0
12*x^2−12=0	±1	Solve for x 12x^2-12=0
1−1/x=0	1	Solve for x 1-1/x=0
3*x^2−3=0	±1	Solve for x 3x^2-3=0
e^(ax)=Ce^(b*x)	ln(C)/(a−b)	Solve for x e^(ax)=Ce^(bx)
x^2+9*x−4=x+2	−4±√(,22)	Solve for x x^2+9x-4=x+2
x^3=0	0	Solve for x x^3=0
0=12x^2−176x+484	11,11/3	Solve for x 0=12x^2-176x+484
2^(2*x)−32⋅2^x+256=0	4	Solve for x 2^(2x)-32*2^x+256=0
y=sec(x)*tan(x)	sin(x)/cos^2(x)	Solve for x y=sec(x)tan(x)
e^x*ln(x)	e^x*ln(x)	Graph e^x natural log of x
y=ln(x√(,x^2−1))	ln(x√(,x^2−1))	Graph natural log of x square root of x^2-1
y=ln(x^4)	d(y)/d(x)=4/x	Differentiate the function
y=2ln(3x)	2ln(3x)	Graph 2 natural log of 3x
z=ln(x^2+y^2)	ln(x^2+y^2)	Graph natural log of x^2+y^2
e^(3*ln(2))	8	Evaluate e^(3 natural log of 2)
ln(x*y)	ln(x)+ln(y)	Graph natural log of xy
(lim_h→0)(((−5+h)^2−25)/h)	−10	Evaluate the Limit
y=3x^3−4x,(1,−1)	5*x−6	Find the Tangent Line at the Point y=3x^3-4x , (1,-1)
y=4x^3−3x,(1,1)	9*x−8	Find the Tangent Line at the Point y=4x^3-3x , (1,1)
(lim_x→0)(sin(4*x)/x)	4	Evaluate the Limit ( limit as x approaches 0 of sin(4x))/x
(lim_x→0)(sin(2x)/sin(3x))	2/3	Evaluate the Limit
(lim_x→1)(((6x−3)^2−9)/(3x−3))	12	Evaluate the Limit
(lim_x→1)((x-1)/(x-1))	1	Evaluate the Limit
(lim_x→0)((x^2−x+sin(x))/(2*x))	0	Evaluate the Limit
y=(7*x)/(x−3),(6,14)	−7/3*x+28	Find the Tangent Line at the Point y=(7x)/(x-3) , (6,14)
2*x^2+y^2=17,(2,3)	−4/3*x+17/3	Find the Tangent Line at the Point 2x^2+y^2=17 , (2,3)
y=x^3,y=4*x	see full solution →	Find the Area Between the Curves y=x^3 , y=4x
y=x^2,y=x+3	(13√(,13))/6	Find the Area Between the Curves y=x^2 , y=x+3
y=7−x^2,y=x+5	9/2	Find the Area Between the Curves y=7-x^2 , y=x+5
y=2*x+24,y=x^2	500/3	Find the Area Between the Curves y=2x+24 , y=x^2
(lim_x→−2)(1/(x+3))	1	Evaluate the Limit limit as x approaches -2 of 1/(x+3)
(lim_x→2)((x^2+4*x−12)/(x^2−4))	2	Evaluate the Limit
(lim_x→π)(sin(x+sin(x)))	0	Evaluate the Limit
(lim_x→2)(g(x))	g(2)	Evaluate the Limit limit as x approaches 2 of g(x)
(lim_x→−∞)(x+√(,x^2+6*x))	−3	Evaluate the Limit
(lim_x→1)(1/x)	1	Evaluate the Limit limit as x approaches 1 of 1/x
(lim_x→3)((√(,x+6)−3)/(x−3))	1/6	Evaluate the Limit
(lim_x→1)(1/(x−1)+1/(x^2−3*x+2))	−1	Evaluate the Limit
(lim_x→10)((x-10)/(x-10))	1	Evaluate the Limit
(lim_x→0^+)(x^2)*ln(x)	0	Evaluate the Limit
(lim_x→0)(1−(x^2)/6)	1	Evaluate the Limit limit as x approaches 0 of 1-(x^2)/6
(lim_y→1)(sec(y*sec^2(y)−tan^2(y)−1))	1	Evaluate the Limit
(lim_x→0)(sin(π/x))	Does Not Exist	Evaluate the Limit limit as x approaches 0 of sin(pi/x)
(lim_x→1)((x-1)/(x-1))	1	Evauate the Limit
(lim_x→0)(sin(3x)/(2x))	3/2	Evaluate the Limit
(lim_x→0)(tan(2*x)/x)	2	Evaluate the Limit limit as x approaches 0 of (tan(2x))/x
(lim_x→∞)(5)*e^x	∞	Evaluate the Limit limit as x approaches infinity of 5e^x
(lim_x→0)(sin(2x)/sin(3x))	2/3	Evaluate the Limit
(lim_x→169)((√(,x)−13)/(x−169))	1/26	Evaluate the Limit
(lim_x→4)((x−4)/(x^2−16))	1/8	Evaluate the Limit
(lim_x→5)((x^2−5x)/(x^2−4x−5))	5/6	Evaluate the Limit
(lim_x→8)(sin(x)/x)	sin(8)/8	Evaluate the Limit ( limit as x approaches 8 of sin(x))/x
(lim_x→64)((√(,x)−8)/(x−64))	1/16	Evaluate the Limit
(lim_x→−6)((x^2−36)/(x+6))	−12	Evaluate the Limit
(lim_x→7)((x^2−49)/(x−7))	14	Evaluate the Limit
(lim_x→3)((x^2−x−6)/(x−3))	5	Evaluate the Limit
(lim_x→4)((4*x−x^2)/(2−√(,x)))	16	Evaluate the Limit
d()/d(x)(5x−x^2)	5 - 2x	Find the Derivative - d/dx y=5x-x^2
(lim_x→3)((x−3)/(x^2−9))	1/6	Evaluate the Limit
(lim_x→1)((x^2+3*x−4)/(x^2−1))	5/2	Evaluate the Limit
(lim_x→1)((x^2+7*x−8)/(x^2−1))	9/2	Evaluate the Limit
(lim_x→1)((2−x)/((x−1)^2))	∞	Evaluate the Limit
(lim_x→10)((x^2−100)/(x−10))	20	Evaluate the Limit
(lim_x→2)((1/x−1/2)/(x−2))	−1/4	Evaluate the Limit
(lim_h→0)((1/((x+h)^2)−1/(x^2))/h)	−2/(x^3)	Evaluate the Limit
(lim_x→3)((x^3−27)/(x−3))	27	Evaluate the Limit
d(√(7,x))/d(x)	1/(7*x^(6/7))	Find the Derivative - d/dx seventh root of x
d^2()/(d(r)^2)(πr^2)	2*π	Multiply (d^2)/(dr^2)*(pir^2)
(∫_^)(5x^2−5x*d(x))	5/3x^3−5/2x^2+C	Find the Antiderivative f(x)=5x^2-5x
(∫_^)(x^4*d(x))	(x^5)/5+C	Find the Antiderivative f(x)=x^4
(∫_^)(sin(3x)d(x))	−1/3cos(3x)+C	Find the Antiderivative sin(3x)
(∫_^)(√(,x)*d(x))	2/3*x^(3/2)+C	Find the Antiderivative f(x) = square root of x
(∫_^)(x^3*d(x))	(x^4)/4+C	Find the Antiderivative f(x)=x^3
(∫_^)(sec^2(x)*d(x))	tan(x)+C	Find the Antiderivative f(x)=sec(x)^2
(∫_^)(4x^2d(x))	(4*x^3)/3+C	Find the Antiderivative 4x^2
(∫_^)(3/x*d(x))	3*ln(x)	Evaluate the Integral
(∫_^)(x^(−1)*d(x))	ln(x)	Evaluate the Integral
ln(3)−ln(1)	ln(3)	Simplify/Condense natural log of 3- natural log of 1
ln(x(x+1)(x+2))	ln(x)+ln(x+1)+ln(x+2)	Expand the Logarithmic Expression natural log of x(x+1)(x+2)
ƒ(x)=sin^2(x)+cos(x)	see full solution →	Find the Local Maxima and Minima f(x)=sin(x)^2+cos(x)
d()/d(x)4x^3	12*x^2	Find the Derivative - d/d@VAR f(x)=4x^3
d()/d(x)4e^x	4*e^x	Find the Derivative - d/d@VAR F(X)=4e^X
d()/d(x)(x^3−3*x^2+4)/(x^2)	(x^3−8)/(x^3)	Find the Derivative - d/d@VAR f(x)=(x^3-3x^2+4)/(x^2)
d(ln(x^3))/d(x)	3/x	Find the Derivative - d/d@VAR f(x) = natural log of x^3
d(ln(x^5))/d(x)	5/x	Find the Derivative - d/d@VAR f(x) = natural log of x^5
d()/d(x)(2x^2+3*x−2)	4*x+3	Find the Derivative - d/d@VAR f(x)=2x^2+3x-2
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative - d/d@VAR f(x)=sec(x)
d()/d(x)1/(x^5)	−5/(x^6)	Find the Derivative - d/d@VAR f(x)=1/(x^5)
x^3+y^3−6xy=0	(2y−x^2)/(y^2−2x)	Find dy/dx x^3+y^3-6xy=0
(∑_k=1^12)(k^2)	650	Evaluate the Summation sum from k=1 to 12 of k^2
y=x^3−6x^2−135x	see full solution →	Find the Local Maxima and Minima y=x^3-6x^2-135x
y=x/(x^2+25)	see full solution →	Find the Local Maxima and Minima y=x/(x^2+25)
ƒ(x)=x^3−27*x	see full solution →	Find the Local Maxima and Minima f(x)=x^3-27x
ƒ(x)=x^2−4*x+5	Local Minimum at *(2,1)	Find the Local Maxima and Minima f(x)=x^2-4x+5
ƒ(x)=x^3−6*x^2+1	see full solution →	Find the Local Maxima and Minima f(x)=x^3-6x^2+1
ƒ(x)=x^4−4*x^3+10	Local Minimum: *(3,−17), Local Maxima: None	Find the Local Maxima and Minima f(x)=x^4-4x^3+10
ƒ(x)=x^4−32*x^2+256	see full solution →	Find the Local Maxima and Minima f(x)=x^4-32x^2+256
ƒ(x)=x^4−50*x^2+625	see full solution →	Find the Local Maxima and Minima f(x)=x^4-50x^2+625
ƒ(x)=3x^4−6x^2+7	see full solution →	Find the Local Maxima and Minima f(x)=3x^4-6x^2+7
(lim_x→4)(1/(x−4))	Does Not Exist	Evaluate the Limit limit as x approaches 4 of 1/(x-4)
(lim_x→0)(x/(x^2−x))	−1	Evaluate the Limit limit as x approaches 0 of x/(x^2-x)
(lim_x→−3)((x^2−9)/(2x^2+7x+3))	6/5	Evaluate the Limit
(lim_x→9)((x^2−9x)/(x^2−8x−9))	9/10	Evaluate the Limit
(lim_x→3)(tan((π*x)/4))	−1	Evaluate the Limit limit as x approaches 3 of tan((pix)/4)
(lim_x→3)(ln(x^2−9))	−∞	Evaluate the Limit
(lim_x→3)(7)	7	Evaluate the Limit limit as x approaches 3 of 7
(lim_x→0)((√(,x+9)−3)/x)	1/6	Evaluate the Limit
(lim_t→∞)(√(,t+t^2)/(7*t−t^2))	0	Evaluate the Limit
(lim_x→1)((x−1)/(x^3−1))	1/3	Evaluate the Limit limit as x approaches 1 of (x-1)/(x^3-1)
(lim_x→16)((x−16)/(√(,x)−4))	8	Evaluate the Limit
(lim_x→5)(ƒ(x))	ƒ(5)	Evaluate the Limit limit as x approaches 5 of f(x)
(lim_x→π)(4)*sin(x+sin(x))	0	Evaluate the Limit
(lim_x→−3)((x^2+6*x+9)/(x^4−81))	0	Evaluate the Limit
x^2−8xy+y^2=8	(4y−x)/(y−4x)	Find dy/dx x^2-8xy+y^2=8
(lim_t→∞)(√(,t+t^2)/(8*t−t^2))	0	Evaluate the Limit
(lim_x→3)((x^2−3x)/(x^2−2x−3))	3/4	Evaluate the Limit
(lim_x→1)((√(,x+3)−2)/(x−1))	1/4	Evaluate the Limit
(lim_x→36)((6−√(,x))/(36*x−x^2))	1/432	Evaluate the Limit
(lim_x→9)((9−x)/(3−√(,x)))	6	Evaluate the Limit
(lim_x→∞)(sin(x)/x)	0	Evaluate the Limit
(lim_x→π)(tan(x))	0	Evaluate the Limit limit as x approaches pi of tan(x)
ƒ(x)=tan((π*x)/2)	see full solution →	Determine if Continuous f(x)=tan((pix)/2)
ƒ(x)=(x^2−16)/(x−4)	(x^2−16)/(x−4)* is discontinuous at *x=4	Determine if Continuous f(x)=(x^2-16)/(x-4)
y=3x^3−36x−2	3x^3−36x−2	Graph y=3x^3-36x-2
y=x^3−6x^2−96x	x^3−6x^2−96x	Graph y=x^3-6x^2-96x
(∫_^)(e^(3x)d(x))	(e^(3*x))/3+C	Find the Antiderivative e^(3x)
ƒ(x)=(x^2−8)/(x+3)	—	Graph f(x)=(x^2-8)/(x+3)
ƒ(x)=ln(x^4+27)	ln(x^4+27)	Graph f(x) = natural log of x^4+27
e^(−x^2)	e^(−x^2)	Graph e^(-x^2)
2*cos(0)	2	Evaluate 2cos(0)
180*(14)−0.30⋅14^3	1696.8	Evaluate 180(14)-0.30*14^3
sec^2(−π/4)	2	Evaluate sec(-pi/4)^2
−6/18^4/6	−1/2916	Evaluate -6/((18^4)/6)
d()/d(θ)*cos(θ^2)	−2θsin(θ^2)	Find the Derivative - d/d@VAR f(theta)=cos(theta^2)
ƒ(x)=2x^3−3x^2−36*x	3, -2	Find the Critical Points f(x)=2x^3-3x^2-36x
ƒ(x)=3x^4−4x^3	0, 1	Find the Critical Points f(x)=3x^4-4x^3
ƒ(x)=e^(1−20x+5x^2)	2	Find the Critical Points f(x)=e^(1-20x+5x^2)
ƒ(x)=x^3+6x^2−15x	−5,1	Find the Critical Points f(x)=x^3+6x^2-15x
x*e^x	−1	Find the Critical Points xe^x
12x^2−176x+484	22/3	Find the Critical Points 12x^2-176x+484
cos(arcsin(5/13))	12/13	Evaluate cos(arcsin(5/13))
sin(4)	sin(4)≈−0.7568	Evaluate sin(4)
d()/d(x)*(e−e^x+x^e)	e*x^(e−1)−e^x	Find the Derivative - d/dx e-e^x+x^e
x^2+y^2=8*x	4, y = -4	Find the Horizontal Tangent Line x^2+y^2=8x
x^2+y^2=2*x	1, y = -1	Find the Horizontal Tangent Line x^2+y^2=2x
y=x^2+1	1	Find the Horizontal Tangent Line y=x^2+1
y=x^2	0	Find the Horizontal Tangent Line y=x^2
x=tan(y)	0⇒No solution	Find Where dy/dx is Equal to Zero x=tan(y)
ƒ(x)=4x^3−34x^2+60*x,0≤x≤2.5	0	Find the Absolute Max and Min over the Interval f(x)=4x^3-34x^2+60x , 0<x<2.5
ƒ(x)=2x^3−12x^2−72*x+2017	6, -2	Find the Critical Points f(x)=2x^3-12x^2-72x+2017
ƒ(x)=x+4/x	−2,2	Find the Critical Points x+4/x
sin(x)	π/2+n*π,n∈ℤ	Find the Critical Points sin(x)
y=x/(x^2+1)	1, -1	Find the Critical Points y=x/(x^2+1)
y=x^3−3x^2−105x	(1,−107)	Find the Inflection Points y=x^3-3x^2-105x
ƒ(x)=x^3−3*x	(0,0)	Find the Inflection Points f(x)=x^3-3x
ƒ(x)=x^4−2*x^2+3	see full solution →	Find the Inflection Points f(x)=x^4-2x^2+3
ƒ(x)=x/(x^2+1)	see full solution →	Find the Concavity f(x)=x/(x^2+1)
d(e^x)/d(x)	e^x	Use the Limit Definition to Find the Derivative e^x
(∫_^)(−cos(x)*d(x))	−sin(x)+C	Find the Antiderivative -cos(x)
d()/d(x)3x^4	12*x^3	Find the Derivative - d/d@VAR f(x)=3x^4
d()/d(x)(x^6)/(1−x^5)	(6*x^5−x^10)/((1−x^5)^2)	Find the Derivative - d/dx y=(x^6)/(1-x^5)
(lim_x→0)((1−cos(x))/(x^2))	1/2	Evaluate the Limit
d()/d(x)*(x/7−7/x)	1/7+7/(x^2)	Find the Derivative - d/dx x/7-7/x
d()/d(u)(u−√(,u))(u+√(,u))	2*u−1	Find the Derivative - d/du
d()/d(x)x/(x^2−9)	−(x^2+9)/((x^2−9)^2)	Find the Derivative - d/d@VAR f(x)=x/(x^2-9)
(∑_i=1^7)(2^(i−1))	127	Evaluate the Summation sum from i=1 to 7 of 2^(i-1)
(∑_i=0^4)(5^i)	781	Evaluate the Summation sum from i=0 to 4 of 5^i
d()/d(x)(∫_^)(√(,x)ln(x)*d(x))	√(,x)*ln(x)	Find the Derivative of the Integral
(∫_^)(xsin(x)d(x))	−x*cos(x)+sin(x)+C	Evaluate the Integral integral of x*sin(x) with respect to x
(∫_^)(5xcos(4x)d(x))	(5x)/4sin(4x)+5/16cos(4*x)+C	Evaluate the Integral integral of 5xcos(4x) with respect to x
d()/d(x)(∫_^)(1/(xln(x))*d(x))	1/(x*ln(x))	Find the Derivative of the Integral
d()/d(x)(5√(,x))/6	5/(12√(,x))	Find the Derivative - d/dx (5 square root of x)/6
24/((5^2+24)^(3/2))	24/343	Evaluate 24/(((5)^2+24)^(3/2))
(1.999)^4	15.968023992001	Evaluate (1.999)^4
(∫_1^7)(x√(,4x^2+9)d(x))	(205√(,205)−13√(,13))/12	Evaluate the Integral
(∫_^)(12xd(x))	6*x^2+C	Evaluate the Integral integral of 12x with respect to x
(∫_^)(14x^6d(x))	2*x^7+C	Evaluate the Integral integral of 14x^6 with respect to x
(∫_^)(14xln(3x)d(x))	7x^2ln(3x)−(7x^2)/2+C	Evaluate the Integral
(∫_2^3)(1/√(,x)−5*d(x))	2√(,3)−2√(,2)−5	Evaluate the Integral
(∫_1^4)(5x^2+√(,x)d(x))	329/3	Evaluate the Integral
(∫_1^4)((e^√(,x))/√(,x)*d(x))	2e^2−2e	Evaluate the Integral
(∫_1^4)(1/√(,t)*d(t))	2	Evaluate the Integral
(∫_1^3)(2/x*d(x))	2*ln(3)	Evaluate the Integral
(∫_^)((x^2)/(x^4−2x^2−8)d(x))	see full solution →	Evaluate the Integral
(∫_−1^2)(9−x^2*d(x))	24	Evaluate the Integral
(∫_−1^1)(√(3,t−2)*d(t))	(3−9√(3,3))/4	Evaluate the Integral
(∫_−1^1)(x*d(x))	0	Evaluate the Integral
(∫_0^2)(3xd(x))	6	Evaluate the Integral
(∫_0^3)((3−t)√(,t)*d(t))	(12√(,3))/5	Evaluate the Integral
(∫_0^4)(x^3*d(x))	64	Evaluate the Integral
(∫_0^3)(35e^td(t))	35*e^3−35	Evaluate the Integral
(∫_0^5)(x√(,25−x^2)*d(x))	125/3	Evaluate the Integral
(∫_0^4)(4x−x^2d(x))	32/3	Evaluate the Integral
(∫_0^8)(x^(1/3)√(,x^(4/3)+9)*d(x))	49	Evaluate the Integral
(∫_0^1)(cos(x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_0^1)(1/(1+x^2)*d(x))	π/4	Evaluate the Integral
(∫_0^1)(e^(−4x)d(x))	(1−e^(−4))/4	Evaluate the Integral
(∫_0^1)(e^(−x^2)*d(x))	see full solution →	Evaluate the Integral
(∫_0^1)(x^11(1+x^12)^11d(x))	455/16	Evaluate the Integral
(∫_0^√(,11))((10x)/√(,x^2+25)d(x))	10	Evaluate the Integral
(∫_0^π/6)(9sec^2(x)d(x))	3√(,3)	Evaluate the Integral
(∫_^)(x(x−1)^5d(x))	((x−1)^7)/7+((x−1)^6)/6+C	Evaluate the Integral integral of x(x-1)^5 with respect to x
(∫_^)(x(2x+5)^8*d(x))	((2x+5)^10)/40−(5(2*x+5)^9)/36+C	Evaluate the Integral integral of x(2x+5)^8 with respect to x
(∫_^)(x*d(y))	x*y+C	Evaluate the Integral integral of x with respect to y
(∫_^)(xarcsin(x)d(x))	((2x^2−1)arcsin(x)+x√(,1−x^2))/4+C	Evaluate the Integral integral of xarcsin(x) with respect to x
(∫_^)(xarctan(x^2)d(x))	1/2x^2arctan(x^2)−1/4*ln(1+x^4)+C	Evaluate the Integral
(∫_^)(xsin(3x^2)*d(x))	−1/6cos(3x^2)+C	Evaluate the Integral integral of xsin(3x^2) with respect to x
(∫_^)(sec(2x)d(x))	1/2ln(abs(sec(2x)+tan(2*x)))+C	Evaluate the Integral
(∫_^)(tan(4x)d(x))	$-\frac{1}{4} \ln	\cos(4x)
(∫_^)(sin(3x)cos(2x)d(x))	−cos(5*x)/10−cos(x)/2+C	Evaluate the Integral
(∫_^)(sin(2t)d(t))	−1/2cos(2t)+C	Evaluate the Integral integral of sin(2t) with respect to t
(∫_^)(sin(2x)cos(x)*d(x))	−2/3*cos^3(x)+C	Evaluate the Integral
(∫_a^b)(5e^(4t)*d(t))	5/4(e^(4b)−e^(4*a))	Evaluate the Integral
(∫_a^b)(ƒ(x)*d(x))	F(b)−F(a)	Evaluate the Integral
(∫_^)(arcsec(x)*d(x))	$x \text{arcsec}(x) - \ln	x + \sqrt{x^2 - 1}
(∫_^)(cot(2x)d(x))	$\frac{1}{2} \ln	\sin(2x)
(∫_^)(csc(2x)d(x))	$\frac{1}{2} \ln	\csc(2x) - \cot(2x)
(∫_e^e^2)(1/(xln(x))d(x))	ln(2)	Evaluate the Integral
(∫_^)(5x^3d(x))	(5*x^4)/4+C	Evaluate the Integral integral of 5x^3 with respect to x
(∫_^)(5xe^(3x)d(x))	5/3xe^(3x)−5/9e^(3*x)+C	Evaluate the Integral integral of 5xe^(3x) with respect to x
(∫_^)(5yd(y))	(5*y^2)/2+C	Evaluate the Integral integral of 5ydy with respect to y
(∫_^)(5sec(x)tan(x)*d(x))	5*sec(x)+C	Evaluate the Integral
(∫_^)(9x^(−5)d(x))	−9/(4*x^4)+C	Evaluate the Integral integral of 9x^-5 with respect to x
(∫_^)(5xcos(2x)d(x))	(5x)/2sin(2x)+5/4cos(2*x)+C	Evaluate the Integral integral of 5xcos(2x) with respect to x
(∫_^)(7xe^x*d(x))	7xe^x−7*e^x+C	Evaluate the Integral integral of 7xe^x with respect to x
(∫_^)(2x√(,x^2+1)d(x))	2/3*(x^2+1)^(3/2)+C	Evaluate the Integral
(∫_−3^−2)(2x(6−x^2)^3*d(x))	65/4	Evaluate the Integral
(∫_^)(2xe^(3x)d(x))	2/3xe^(3x)−2/9e^(3*x)+C	Evaluate the Integral integral of 2xe^(3x) with respect to x
(∫_^)(2x^2√(4,5+4x^3)*d(x))	2/15(5+4x^3)^(5/4)+C	Evaluate the Integral
(∫_^)(3√(3,x^2)*d(x))	9/5*x^(5/3)+C	Evaluate the Integral
(∫_^)(3t^2√(,t^3+2)d(t))	(2*(t^3+2)^(3/2))/3+C	Evaluate the Integral
(∫_^)(xe^(−5x)*d(x))	−1/5xe^(−5x)−1/25e^(−5*x)+C	Evaluate the Integral integral of xe^(-5x) with respect to x
(∫_^)(xe^(3x^2)*d(x))	1/6e^(3x^2)+C	Evaluate the Integral integral of xe^(3x^2) with respect to x
(∫_0^π/2)(sin(2x)d(x))	1	Evaluate the Integral
(∫_0^π/3)(5sec^2(x)d(x))	5√(,3)	Evaluate the Integral
(∫_^)((x+3)/(x^2+6x+7)d(x))	$\frac{1}{2} \ln	x^2+6x+7
(∫_^)(x^3√(,x^2−1)*d(x))	1/5(x^2−1)^(5/2)+1/3(x^2−1)^(3/2)+C	Evaluate the Integral
(∫_^)(√(,6x)d(x))	(2√(,6))/3*x^(3/2)+C	Evaluate the Integral
(∫_^)(√(,4x+9)d(x))	1/6(4x+9)^(3/2)+C	Evaluate the Integral
(∫_^)(√(,2x−1)d(x))	1/3(2x−1)^(3/2)+C	Evaluate the Integral
(∫_^)(√(,2x−3)d(x))	1/3(2x−3)^(3/2)+C	Evaluate the Integral
(∫_^)((−x)/((x+1)−√(,x+1))*d(x))	−x−2√(,x+1)+C	Evaluate the Integral
(∫_^)(x/√(,2x−1)d(x))	1/6(2x−1)^(3/2)+1/2(2x−1)^(1/2)+C	Evaluate the Integral
(∫_^)(x^2√(,1+x^3)*d(x))	2/9*(1+x^3)^(3/2)+C	Evaluate the Integral
(∫_^)(x^2ln(3x)*d(x))	(x^3ln(3x))/3−(x^3)/9+C	Evaluate the Integral
(∫_^)(x^2(x^3−1)^4d(x))	((x^3−1)^5)/15+C	Evaluate the Integral
(∫_^)(x^2e^xd(x))	e^x(x^2−2x+2)+C	Evaluate the Integral integral of x^2*e^x with respect to x
(∫_^)(x^2e^(−x)d(x))	−e^(−x)(x^2+2x+2)+C	Evaluate the Integral integral of x^2*e^(-x) with respect to x
(∫_^)(x/(x^2−4)*d(x))	$\frac{1}{2} \ln	x^2-4
(∫_^)(x^11ln(x)d(x))	(x^12*ln(x))/12−(x^12)/144+C	Evaluate the Integral
(∫_^)(x^(5/2)*d(x))	2/7*x^(7/2)+C	Evaluate the Integral integral of x^(5/2) with respect to x
(∫_^)(e^(−6x)d(x))	−1/6e^(−6x)+C	Evaluate the Integral integral of e^(-6x) with respect to x
d(√(6,x))/d(x)	1/(6*x^(5/6))	Find the Derivative - d/d@VAR f(x) = sixth root of x
(∫_^)(e^xcos(x)d(x))	(e^x*(cos(x)+sin(x)))/2+C	Evaluate the Integral integral of e^x*cos(x) with respect to x
(∫_^)(ln(x)/(x^5)*d(x))	−(4ln(x)+1)/(16x^4)+C	Evaluate the Integral
(∫_^)(e^(−2t)d(t))	−1/2e^(−2t)+C	Evaluate the Integral integral of e^(-2t) with respect to t
(∫_^)(e^(x^2)/2*d(x))	see full solution →	Evaluate the Integral
(∫_^)(csc^2(3x)d(x))	−1/3cot(3x)+C	Evaluate the Integral integral of csc(3x)^2 with respect to x
(∫_^)(sin^4(x)cos^3(x)d(x))	sin^5(x)/5−sin^7(x)/7+C	Evaluate the Integral
(∫_^)(√(,x^2+4)*d(x))	$\frac{x \sqrt{x^2+4}}{2} + 2 \ln	x + \sqrt{x^2+4}
(∫_^)(te^(t^2)d(t))	1/2*e^(t^2)+C	Evaluate the Integral integral of te^(t^2) with respect to t
(∫_^)(√(,x^11)*d(x))	(2*x^(13/2))/13+C	Evaluate the Integral
(∫_^)(sec^6(x)*d(x))	tan(x)+2/3tan^3(x)+1/5tan^5(x)+C	Evaluate the Integral integral of sec(x)^6 with respect to x
(∫_^)(sec(x)/tan(x)*d(x))	$-\ln	\csc(x) + \cot(x)
(∫_^)(3/(x^3)*d(x))	−3/(2*x^2)+C	Evaluate the Integral integral of 3/(x^3) with respect to x
(∫_^)(2/(x^2+1)*d(x))	2*arctan(x)+C	Evaluate the Integral integral of 2/(x^2+1) with respect to x
(∫_^)(2/(x−2)*d(x))	$2 \ln	x-2
(∫_^)((1−cos(2x))/2d(x))	x/2−sin(2*x)/4+C	Evaluate the Integral
(∫_^)(cos^2(x)tan^3(x)d(x))	$\frac{\cos^2(x)}{2} - \ln	\cos(x)
(∫_^)((x^4)/(x−1)*d(x))	see full solution →	Evaluate the Integral
(∫_^)((x^4−3x^2+5)/(x^4)d(x))	x+3/x−5/(3*x^3)+C	Evaluate the Integral
(∫_^)((x^9)/(1+x^20)*d(x))	1/10*arctan(x^10)+C	Evaluate the Integral
(∫_^)((x^2)/(4+x^2)*d(x))	x−2*arctan(x/2)+C	Evaluate the Integral
(∫_^)(1/√(,8x)d(x))	√(,2*x)/2+C	Evaluate the Integral
(∫_^)(1/√(,1−9x^2)d(x))	1/3arcsin(3x)+C	Evaluate the Integral
(∫_^)(1/√(,4+x^2)*d(x))	$\ln	x + \sqrt{4+x^2}
(∫_^)(1/√(,x^2−25)*d(x))	$\ln	x + \sqrt{x^2 - 25}
(∫_^)(1/(x^13)*d(x))	−1/(12*x^12)+C	Evaluate the Integral integral of 1/(x^13) with respect to x
(lim_x→1)((x^4−1)/(x−1))	4	Evaluate the Limit limit as x approaches 1 of (x^4-1)/(x-1)
(∫_^)(1/(x√(,x^2−4))*d(x))	1/2*arcsec(x/2)+C	Evaluate the Integral
(∫_^)(1/(2x+5)d(x))	$\frac{1}{2} \ln	2x+5
(∫_^)(1/(2y)d(y))	$\frac{1}{2} \ln	y
(∫_^)(1/(2x−1)d(x))	$\frac{1}{2}\ln	2x-1
(∫_^)(1/(2x)d(x))	$\frac{1}{2} \ln	x
(∫_^)(1/5sin(5x)*d(x))	−1/25cos(5x)+C	Evaluate the Integral
(∫_^)(1/(3x+5)d(x))	$\frac{1}{3} \ln	3x+5
(∫_^)(1/(3x−2)d(x))	$\frac{1}{3} \ln	3x-2
(∫_^)(1/(4x^6)d(x))	−1/(20*x^5)+C	Evaluate the Integral integral of 1/(4x^6) with respect to x
d^2()/(d(x)^2)*(sin(x)+cos(x))	−sin(x)−cos(x)	Find the 2nd Derivative sin(x)+cos(x)
d^2()/(d(x)^2)√(,x^2+1)	1/((x^2+1)^(3/2))	Find the 2nd Derivative y = square root of x^2+1
(∫_^)(3x^8−7x^3+7*d(x))	1/3x^9−7/4x^4+7*x+C	Evaluate the Integral
(∫_^)(2x−7d(x))	x^2−7*x+C	Evaluate the Integral integral of 2x-7 with respect to x
(∫_^)((1+3t)t^2*d(t))	1/3t^3+3/4t^4+C	Evaluate the Integral integral of (1+3t)t^2 with respect to t
(∫_^)(5e^z+4d(z))	5e^z+4z+C	Evaluate the Integral integral of 5e^z+4 with respect to z
(∫_^)(4x−5d(x))	2x^2−5x+C	Evaluate the Integral integral of 4x-5 with respect to x
d^4(sin(x))/(d(x)^4)	sin(x)	Find the 4th Derivative f(x)=sin(x)
(∫_^)(12/√(,x)+12√(,x)*d(x))	24√(,x)+8*x√(,x)+C	Evaluate the Integral
(∫_^)(x^2−7x+3d(x))	(x^3)/3−(7x^2)/2+3x+C	Evaluate the Integral integral of x^2-7x+3 with respect to x
(∫_^)((1−2x)^9d(x))	−((1−2*x)^10)/20+C	Evaluate the Integral integral of (1-2x)^9 with respect to x
(∫_^)(ln(x)/x*d(x))	ln(x)/7+C	Evaluate the Integral
(∫_^)(ln(x)/x*d(x))	ln(x)/5+C	Evaluate the Integral
(∫_^)((e^(2x))/(1+e^(2x))*d(x))	1/2ln(1+e^(2x))+C	Evaluate the Integral
(∫_^)(sin^4(x)*d(x))	(3x)/8−sin(2x)/4+sin(4*x)/32+C	Evaluate the Integral integral of sin(x)^4 with respect to x
(lim_x→8)(ln(x)/√(,x))	(3*ln(2))/(2√(,2))	Evaluate Using L'Hospital's Rule
(lim_x→π/2)(cos(x)/(1−sin(x)))	∞	Evaluate Using L'Hospital's Rule
(∑_k=5^26)(4)	$5}^{26} 4 = 88$	Evaluate the Summation sum from k=5 to 26 of 4
(∑_n=1^14)(3*n+2)	$1}^{14} (3n + 2) = 343$	Evaluate the Summation sum from n=1 to 14 of 3n+2
(∑_n=1^8)(1/n)	$1}^{8} \frac{1}{n} = \frac{761}{280}$	Evaluate the Summation sum from n=1 to 8 of 1/n
(∑_n=1^8)(−)4(1/3)^(n−1)	see full solution →	Evaluate the Summation sum from n=1 to 8 of -4(1/3)^(n-1)
(∑_i=5^13)(3*i+2)	$5}^{13} (3i + 2) = 261$	Evaluate the Summation sum from i=5 to 13 of 3i+2
(∑_i=1^10)(i)*(i^2+1)	$1}^{10} i(i^2+1) = 3080$	Evaluate the Summation sum from i=1 to 10 of i(i^2+1)
d^2()/(d(x)^2)√(,x+11)	−1/(4*(x+11)^(3/2))	Find the 2nd Derivative y = square root of x+11
d^2()/(d(x)^2)*(−x/y)	see full solution →	Find the 2nd Derivative -x/y
d^2(sec^2(x))/(d(x)^2)	4sec^2(x)tan^2(x)+2*sec^4(x)	Find the 2nd Derivative sec(x)^2
d(ln(tan(x)))/d(x)	2csc(2x)	Find the Derivative - d/dx natural log of tan(x)
d(cos(x^2))/d(x)	−2xsin(x^2)	Find the Derivative - d/dx y=cos(x^2)
d(√(,x^7))/d(x)	7/2*x^(5/2)	Find the Derivative - d/dx square root of x^7
d(cos(x))/d(x)	−9cos(x)sin(x)	Find the Derivative - d/dx cos(x)^9
d()/d(x)*8	0	Find the Derivative - d/dx y=8
d()/d(x)(2x−7)^4*(x^2+x+1)^5	(2x−7)^3(x^2+x+1)^4(28x^2−52*x−27)	Find the Derivative - d/dx (2x-7)^4(x^2+x+1)^5
d(cos(2*x))/d(x)	−2sin(4x)	Find the Derivative - d/dx cos(2x)^2
d()/d(x)9/x	−9/(x^2)	Find the Derivative - d/dx 9/x
d(ln(x^5))/d(x)	5/x	Find the Derivative - d/dx natural log of x^5
d()/d(x)x^2e^(3*x)	xe^(3x)(3x+2)	Find the Derivative - d/dX x^2e^(3x)
d()/d(x)1/2xe^(−1/2*x)	1/2e^(−1/2x)−1/4xe^(−1/2*x)	Find the Derivative - d/dx 1/2*(xe^(-1/2x))
d()/d(x)(4x^2−5*x)	8*x−5	Find the Derivative - d/dx y=4x^2-5x
(∫_^)(√(3,x^11)*d(x))	(3*x^14/3)/14+C	Evaluate the Integral
(lim_x→0)(tan(x))	0	Evaluate the Limit limit as x approaches 0 of tan(x)
(lim_x→π)(sin(x−sin(x)))	0	Evaluate the Limit
(lim_h→0)((2(x+h)−2x)/h)	2	Evaluate the Limit
d(cos(2*t))/d(t)	−2sin(2t)	Find the Derivative - d/dt cos(2t)
(∫_^)(1/√(,4−9x^2)d(x))	1/3arcsin((3x)/2)+C	Evaluate the Integral
(lim_x→0)((1/(2+x)−1/2)/x)	−1/4	Evaluate the Limit
(lim_x→8)(√(,x))	2√(,2)	Evaluate the Limit
(lim_x→∞)(1/x)	0	Evaluate the Limit limit as x approaches infinity of 1/x
(lim_x→∞)(1−4/x)	e^(−4)	Evaluate the Limit limit as x approaches 8 of (1-4/x)^x
(lim_x→8)((5x^2+7x−9)/(−6*x^2+2))	−367/382	Evaluate the Limit
(lim_x→6)((x^3−36*x)/(x−6))	72	Evaluate the Limit
(lim_x→5)(x)	5	Evaluate the Limit limit as x approaches 5 of x
(lim_x→4)((x−4)/(x^3−64))	1/48	Evaluate the Limit
(lim_x→5)(1/(x−5))	Does not exist	Evaluate the Limit limit as x approaches 5 of 1/(x-5)
(lim_x→−1)((2x^2+3x+1)/(x^2−2*x−3))	1/4	Evaluate the Limit
(lim_x→9)((x^2−81)/(x−9))	18	Evaluate the Limit
(lim_x→−∞)(x^6+x^7)	−∞	Evaluate the Limit
(lim_x→∞)(√(,x+x^2)/(2*x−x^2))	0	Evaluate the Limit
(lim_x→144)((√(,x)−12)/(x−144))	1/24	Evaluate the Limit
(lim_x→−7)((x^2−49)/(x+7))	−14	Evaluate the Limit
(lim_x→∞)((5*x^3+1)/(x−x^3))	−5	Evaluate the Limit
(lim_x→3)(ln(x−3))	−∞	Evaluate the Limit
(d(x^12)*e^x)/d(x)	x^11e^x(x+12)	Find the Derivative - d/dx x^12e^x
(lim_h→0)((√(,25+h)−5)/h)	1/10	Evaluate the Limit
(lim_t→∞)(√(,t+t^2)/(3*t−t^2))	0	Evaluate the Limit
(lim_h→0)((√(,16+h)−4)/h)	1/8	Evaluate the Limit
(lim_x→∞)(√(,x+x^2)/(5*x−x^2))	0	Evaluate the Limit
(lim_x→5)(12)	12	Evaluate the Limit limit as x approaches 5 of 12
(lim_x→−1)((2*x^2−x−3)/(x+1))	−5	Evaluate the Limit
(lim_x→4)(g(x))	g(4)	Evaluate the Limit limit as x approaches 4 of g(x)
d()/d(x)*(a^9+cos^9(x))	−9sin(x)cos^8(x)	Find the Derivative - d/dx a^9+cos(x)^9
ƒ(x)=2x^3−3x^2−36*x	see full solution →	Find the Local Maxima and Minima f(x)=2x^3-3x^2-36x
ƒ(x)=4x^3−12x	see full solution →	Find the Local Maxima and Minima f(x)=4x^3-12x
ƒ(x)=5x^3−15x	see full solution →	Find the Local Maxima and Minima f(x)=5x^3-15x
d()/d(x)√(3,6*x^2+1)	(4x)/√(3,(6x^2+1)^2)	Find the Derivative - d/dx y = cube root of 6x^2+1
ƒ(x)=x^3−6*x^2	see full solution →	Find the Local Maxima and Minima f(x)=x^3-6x^2
ƒ(x)=x^5*ln(x)	see full solution →	Find the Local Maxima and Minima f(x)=x^5 natural log of x
ƒ(x)=x^2*ln(x)	see full solution →	Find the Local Maxima and Minima f(x)=x^2 natural log of x
ƒ(x)=x^2−4*x+7	Local Minimum: *(2,3), Local Maxima: None	Find the Local Maxima and Minima f(x)=x^2-4x+7
ƒ(x)=x^2+4*x+5	Local Minimum at *(−2,1), No Local Maxima	Find the Local Maxima and Minima f(x)=x^2+4x+5
d()/d(x)(x+7)(x^2−7)	3x^2+14x−7	Find dy/dx y=(x+7)(x^2-7)
ƒ(x)=x^3−3*x^2+3	see full solution →	Find the Local Maxima and Minima f(x)=x^3-3x^2+3
d()/d(x)(7√(,x))/8	7/(16√(,x))	Find the Derivative - d/dx y=(7 square root of x)/8
y=x^4−2*x^2	see full solution →	Find the Local Maxima and Minima y=x^4-2x^2
y=(x^2−5)/(x−3)	Local Maxima: (1,2), Local Minima: (5,10)	Find the Local Maxima and Minima y=(x^2-5)/(x-3)
(d(7)*x^3)/d(x)	21*x^2	Find the Derivative - d/dx 7x^3
ƒ(x)=x+2*cos(x)	see full solution →	Find the Local Maxima and Minima f(x)=x+2cos(x)
ƒ(x)=cos(π*x)	see full solution →	Find the Local Maxima and Minima f(x)=cos(pix)
ƒ(x)=ln(x^4+27)	see full solution →	Find the Local Maxima and Minima f(x) = natural log of x^4+27
d()/d(x)*(−sin(x))	−cos(x)	Find the Derivative - d/d@VAR f(x)=-sin(x)
d(sin(ln(x)))/d(x)	cos(ln(x))/x	Find the Derivative - d/d@VAR f(x)=sin( natural log of x)
d(sin(π*x))/d(x)	πcos(πx)	Find the Derivative - d/d@VAR f(x)=sin(pix)
d()/d(x)(4x+1)^2	8(4x+1)	Find the Derivative - d/d@VAR F(x)=(4x+1)^2
d()/d(x)*(x^2+4)	2*x	Find the Derivative - d/d@VAR f(x)=x^2+4
d()/d(x)5e^x	5*e^x	Find the Derivative - d/d@VAR f(x)=5e^x
d()/d(x)2x^4	8*x^3	Find the Derivative - d/d@VAR f(x)=2x^4
d()/d(x)6x^3	18*x^2	Find the Derivative - d/d@VAR f(x)=6x^3
d()/d(x)√(,2−6*x)	(−3)/√(,2−6*x)	Find the Derivative - d/d@VAR f(x) = square root of 2-6x
d()/d(x)2e^(3*x−1)	6e^(3x−1)	Find the Derivative - d/d@VAR f(x)=2e^(3x-1)
d()/d(x)*(x^2+x−5)	2*x+1	Find the Derivative - d/d@VAR f(x)=x^2+x-5
d()/d(x)√(,7x+√(,7x+√(,7*x)))	see full solution →	Find the Derivative - d/dx
ƒ(x)=(x^2−1)^3	Local Minimum: *(0,−1), Local Maxima: None	Find the Local Maxima and Minima f(x)=(x^2-1)^3
ƒ(x)=x^3−12*x+2	see full solution →	Find the Local Maxima and Minima x^3-12x+2
(∫_^)(−x^2*d(x))	−(x^3)/3+C	Find the Antiderivative -x^2
( \int	x	,dx )
(∫_^)(2/x*d(x))	$2 \ln	x
(∫_^)(arctan(x)*d(x))	xarctan(x)−1/2ln(1+x^2)+C	Find the Antiderivative arctan(x)
(∫_^)(3x^3d(x))	3/4*x^4+C	Find the Antiderivative 3x^3
(∫_^)(5x^2d(x))	(5*x^3)/3+C	Find the Antiderivative 5x^2
(∫_^)(e^(2x)d(x))	(e^(2*x))/2+C	Find the Antiderivative f(x)=e^(2x)
(∫_^)(x^(1/3)*d(x))	3/4*x^(4/3)+C	Find the Antiderivative f(x)=x^(1/3)
(∫_^)(1/2x^2−2x+6*d(x))	1/6x^3−x^2+6x+C	Find the Antiderivative f(x)=1/2x^2-2x+6
(∫_^)(x(2−x)^2d(x))	2x^2−(4x^3)/3+(x^4)/4+C	Find the Antiderivative f(x)=x(2-x)^2
(∫_^)(18x^5d(x))	3*x^6+C	Find the Antiderivative f(x)=18x^5
(∫_^)(144−x^2*d(x))	144*x−(x^3)/3+C	Find the Antiderivative f(x)=144-x^2
(∫_^)(3xd(x))	(3*x^2)/2+C	Find the Antiderivative f(x)=3x
y=(2x+1)^(4x)	(2x+1)^(4x)(4ln(2x+1)+(8x)/(2*x+1))	Find dy/dx y=(2x+1)^(4x)
ƒ(x)=5*x^2	10x+5h	Find the Difference Quotient f(x)=5x^2
d()/d(x)*(e^x−cot(x))	e^x+csc^2(x)	Find the Derivative - d/dx e^x-cot(x)
(lim_h→0)(((x+h)^2−x^2)/h)	2*x	Evaluate the Limit
(lim_h→0)(h+2*x+1)	2*x+1	Evaluate the Limit limit as h approaches 0 of h+2x+1
(lim_x→∞)(ƒ(x)+2*g(x))	(lim_x→∞)(ƒ(x))+2*(lim_x→∞)(g(x))	Evaluate the Limit
(lim_t→0)(5/(t√(,1+t))−5/t)	−5/2	Evaluate the Limit
(lim_x→2)((x^2−5*x+6)/(x−2))	−1	Evaluate the Limit
(lim_x→0)(1/x−1/(x^2+x))	1	Evaluate the Limit limit as x approaches 0 of 1/x-1/(x^2+x)
(lim_x→2)((√(,x+2)−2)/(x−2))	1/4	Evaluate the Limit
(lim_x→16)((4−√(,x))/(16*x−x^2))	1/128	Evaluate the Limit
(lim_x→1)((x−1)/(√(,x)−1))	2	Evaluate the Limit
(lim_x→100)((√(,x)−10)/(x−100))	1/20	Evaluate the Limit
( \lim_{x \to -2} \frac{	x+2	}{x+2} )
(lim_x→2)((1/x−1/2)/(x−2))	−1/4	Evaluate the Limit
(lim_x→−1)((2*x^2−x−3)/(x+1))	−5	Evaluate the Limit
(lim_x→−1)((6x+5)/(5x−6))	1/11	Evaluate the Limit
(lim_x→−4)((1/4+1/x)/(4+x))	−1/16	Evaluate the Limit
(lim_x→3)((x^3−27)/(x^2−9))	9/2	Evaluate the Limit
(lim_x→3)((x^3−27)/(x−3))	27	Evaluate the Limit
(lim_x→3)((x^3−9*x)/(x−3))	18	Evaluate the Limit
(lim_x→−3)((x^2+x−6)/(x^2−9))	5/6	Evaluate the Limit
(lim_x→2)((x^5−32)/(x−2))	80	Evaluate the Limit
(lim_x→2)((x−3)/(x−2))	Does Not Exist	Evaluate the Limit ( limit as x approaches 2 of x-3)/(x-2)
(lim_x→5)((x^3−125)/(x−5))	75	Evaluate the Limit
(lim_x→5)((x^3−125)/(x−5))	75	Evaluate the Limit
(lim_x→8)((√(3,x)−2)/(x−8))	1/12	Evaluate the Limit
(lim_x→9)((9−x)/(√(,x)−3))	−6	Evaluate the Limit
(lim_x→a)((x^2−a^2)/(x−a))	2*a	Evaluate the Limit
(lim_x→0)((2^x−1)/x)	ln(2)	Evaluate the Limit limit as x approaches 0 of (2^x-1)/x
(lim_x→0)(1−8*x)	e^(−8)	Evaluate the Limit limit as x approaches 0 of (1-8x)^(1/x)
(lim_x→0)((x^2−x)/x)	−1	Evaluate the Limit limit as x approaches 0 of (x^2-x)/x
(lim_x→0)(2*sin(x)−1)	−1	Evaluate the Limit limit as x approaches 0 of 2sin(x)-1
(lim_h→0)((ƒ*(x+h)−ƒ(x))/h)	ƒ(x)^′	Evaluate the Limit
(lim_h→0)((√(,36+h)−6)/h)	1/12	Evaluate the Limit
(lim_x→0)(sin(2x)/sin(5x))	2/5	Evaluate the Limit
(lim_x→0)(sin(5x)/sin(2x))	5/2	Evaluate the Limit
(lim_x→4)((x^2+3*x−28)/(x^2−16))	11/8	Evaluate the Limit
( \lim_{x \to 0} \frac{\sin(x)}{	x	} )
(lim_x→0)(sin(9*x)/x)	9	Evaluate the Limit limit as x approaches 0 of (sin(9x))/x
(lim_x→0)((tan(x)−x)/(x^3))	1/3	Evaluate the Limit
(lim_x→0)(tan(5*x)/x)	5	Evaluate the Limit limit as x approaches 0 of (tan(5x))/x
(lim_x→0)(e^1/x)	Does Not Exist	Evaluate the Limit limit as x approaches 0 of e^(1/x)
(lim_x→0)(2/x)	Does Not Exist	Evaluate the Limit limit as x approaches 0 of 2/x
(lim_x→0)(x)*cos(x)	0	Evaluate the Limit limit as x approaches 0 of xcos(x)
(lim_x→0)((x−3)/(x^2−3*x))	Does Not Exist	Evaluate the Limit
(lim_x→0)(3)	3	Evaluate the Limit limit as x approaches 0 of 3
(lim_x→0)(x^4)*cos(2/x)	0	Evaluate the Limit limit as x approaches 0 of x^4cos(2/x)
(lim_x→0)(g(x))	g(0)	Evaluate the Limit limit as x approaches 0 of g(x)
(lim_x→196)((√(,x)−14)/(x−196))	1/28	Evaluate the Limit
(lim_x→1)(2/2)(16x−12)	4	Evaluate the Limit limit as x approaches 1 of 2/2*(16x-12)
(lim_x→0)((√(,9+x)−3)/x)	1/6	Evaluate the Limit
(lim_x→1)(5)	5	Evaluate the Limit limit as x approaches 1 of 5
(lim_x→1)(g(x))	L	Evaluate the Limit limit as x approaches 1 of g(x)
(lim_x→1)(x/(x−1)−1/ln(x))	1/2	Evaluate the Limit
(lim_x→−2)((x^3+8)/(x^2+8*x+12))	3	Evaluate the Limit
( \lim_{x \to 1}	x-1	)
(lim_x→7)((x^2−7x)/(x^2−6x−7))	7/8	Evaluate the Limit
(lim_x→−2)((x^2+4*x+4)/(x^4−16))	0	Evaluate the Limit
(lim_x→−2)(√(,7*x^4+x^2))	2√(,29)	Evaluate the Limit
(lim_x→2)(ln(x−2))	−∞	Evaluate the Limit
(lim_x→2)(3*x+2)	8	Evaluate the Limit limit as x approaches 2 of 3x+2
(lim_x→−5)((x^3+125)/(x+5))	75	Evaluate the Limit
(lim_x→2)(x^3+5x^2−7x+1)	15	Evaluate the Limit limit as x approaches 2 of x^3+5x^2-7x+1
(lim_x→−2)(3x^5−3x^4+4*x^3+x^2+5)	−167	Evaluate the Limit
y=4−x^2,y=x+2	9/2	Find the Area Between the Curves y=4-x^2 , y=x+2
y=4−x^2,y=x−2	125/6	Find the Area Between the Curves y=4-x^2 , y=x-2
y=x^(5/4),y=3*x^(1/4)	(16⋅3^(1/4))/5	Find the Area Between the Curves y=x^(5/4) , y=3x^(1/4)
y=1−x^2,y=0	(16*π)/15	Find the Volume y=1-x^2 , y=0
2*x^2+y^2=12,(2,−2)	2*x−6	Find the Tangent Line at the Point 2x^2+y^2=12 , (2,-2)
2*x^2+y^2=57,(−4,5)	8/5*x+57/5	Find the Tangent Line at the Point 2x^2+y^2=57 , (-4,5)
y=(7*x)/(x+4),(3,3)	4/7*x+9/7	Find the Tangent Line at the Point y=(7x)/(x+4) , (3,3)
y=(7*x)/(x−1),(2,14)	−7*x+28	Find the Tangent Line at the Point y=(7x)/(x-1) , (2,14)
y=(4*x)/(x−5),(7,14)	−5*x+49	Find the Tangent Line at the Point y=(4x)/(x-5) , (7,14)
y=√(,2*x),(18,6)	1/6*x+3	Find the Tangent Line at the Point y = square root of 2x , (18,6)
y=√(,x),(1,1)	1/2*x+1/2	Find the Tangent Line at the Point y = square root of x , (1,1)
(lim_x→0)((√(,3+x)−√(,3))/x)	√(,3)/6	Evaluate the Limit
(lim_x→0)(((2+x)^3−8)/x)	12	Evaluate the Limit
(lim_x→0)((x^3−6*x+8)/(x−2))	−4	Evaluate the Limit
(lim_x→0)((3*(1−cos(x)))/x)	0	Evaluate the Limit
(lim_x→0)((cos(x)−1)/x)	0	Evaluate the Limit ( limit as x approaches 0 of cos(x)-1)/x
(lim_x→0)(sin(x^2)/x)	0	Evaluate the Limit ( limit as x approaches 0 of sin(x^2))/x
(lim_x→0)(sin(5x)/(2x))	5/2	Evaluate the Limit
(lim_a→0)(sin(a)/a)	1	Evaluate the Limit ( limit as a approaches 0 of sin(a))/a
(lim_x→0)((tan(x)−x)/(x^3))	1/3	Evaluate the Limit
(lim_x→0)((sin(x)cos(4x))/(x+xcos(5x)))	1/2	Evaluate the Limit
(lim_x→0)(tan(2*x)/x)	2	Evaluate the Limit ( limit as x approaches 0 of tan(2x))/x
y=4x^3−4x,(−1,0)	8*x+8	Find the Tangent Line at the Point y=4x^3-4x , (-1,0)
y=16√(,x),(16,64)	2*x+32	Find the Tangent Line at the Point y=16 square root of x , (16,64)
sin(ln(x))	sin(ln(x))	Graph sin( natural log of x)
ƒ(x)=3xln(x)	3xln(x)	Graph 3x natural log of x
cos(ln(x))	cos(ln(x))	Graph cos( natural log of x)
y=ln(9*x)	ln(9*x)	Graph natural log of 9x
y=ln(sec(x))	ln(sec(x))	Graph natural log of sec(x)
y=ln(6*x)	ln(6*x)	Graph natural log of 6x
ƒ(x)=1/(x*ln(x))	1/(x*ln(x))	Graph 1/(x natural log of x)
ƒ(x)=x/ln(x)	x/ln(x)	Graph x/( natural log of x)
ln(x^3)	ln(x^3)	Graph natural log of (x)^3
ln(ln(e^(e^8)))	8	Evaluate natural log of natural log of e^(e^8)
2*ln(3)	ln(9)	Evaluate 2 natural log of 3
ln(3*e^2)	ln(3)+2	Evaluate natural log of 3e^2
ƒ(g(x−1))* where ƒ(x)=x^2,g(x)=2x+5,h(x)=x^2−1	4x^2+12x+9	Solve the Function Operation
( \int_{-2}^{1}	2x - (x^2 - 3)	,dx ) $
d(2^5)/d(x)	0	Find the Derivative - d/dx 2^5
tan(x)=−4/5	see full solution →	Solve for x tan(x)=-4/5
sin(o)=5/6	see full solution →	Solve for o sin(o)=5/6
3x^2−4x−4=0	2,−2/3	Solve for x 3x^2-4x-4=0
4*x−36/x=0	±3	Solve for x 4x-36/x=0
−12x^2+48x=0	0⇒x=0,4	Solve for x -12x^2+48x=0
12x^2−120x+209=0	5±√(,273)/6	Solve for x 12x^2-120x+209=0
12x^2−264x+989=0	—	Solve for x 12x^2-264x+989=0
2*x^(−3)=0	0⇒No solution	Solve for x 2x^-3=0
ln(x)−ln(x^2)+ln(3)=0	0⇒x=3	Solve for x
ln(x)=0	0⇒x=1	Solve for x natural log of x=0
ln(x^2+1)−3*ln(x)=ln(2)	ln(2)⇒x=1	Solve for x
6x^2−2x−4=0	1,−2/3	Solve for x 6x^2-2x-4=0
e^(x^2)	e^(x^2)	Simplify e^(x^2)
(e^(1/x))/(x^2)	x^(−2)*e^(1/x)	Simplify (e^(1/x))/(x^2)
(x^(r/s()))^(s/r)	x	Simplify (x^(r/s))^(s/r)
(x^2−1)^3	x^6−3x^4+3x^2−1	Simplify (x^2-1)^3
(e^x+e^(−x))^2	e^(2x)+2+e^(−2x)	Simplify (e^x+e^(-x))^2
(e^x−e^(−x))^2	e^(2x)−2+e^(−2x)	Simplify (e^x-e^(-x))^2
(π/2)^2	(π^2)/4	Simplify (pi/2)^2
cos(x)=x^4−x	x^4−x⇒x≈−0.7050,1.1163	Solve for x cos(x)=x^4-x
x^3+y^3=12xy−8	(4y−x^2)/(y^2−4x)	Find dy/dx x^3+y^3=12xy-8
tan(x)/x	sin(x)/(x*cos(x))	Simplify (tan(x))/x
sec(0)	1	Simplify sec(0)^2
x(99−x)(66−2*x)	2x^3−264x^2+6534*x	Simplify x(99-x)(66-2x)
x(27−x)(18−2*x)	2x^3−72x^2+486*x	Simplify x(27-x)(18-2x)
d(x^2+4)/d(x)	10x(x^2+4)^4	Find the Derivative - d/dx (x^2+4)^5
d(4*x−5)/d(x)	32*x−40	Find the Derivative - d/dx (4x-5)^2
d()/d(x)3e^x*cos(x)	3e^x(cos(x)−sin(x))	Find the Derivative - d/dx 3e^xcos(x)
d()/d(x)*(x^3−8)^4	12x^2(x^3−8)^3	Find the Derivative - d/dx (x^3-8)^4
d()/d(x)*x√(,x−1)	(3*x−2)/(2√(,x−1))	Find the Derivative - d/dx x square root of x-1
d(√(,16−x^2))/d(x)	−x/√(,16−x^2)	Find the Derivative - d/dx square root of 16-x^2
d()/d(t)1/t	−1/(t^2)	Find the Derivative - d/dt 1/t
d()/d(t)699/((t+1)^0.94)	−657.06/((t+1)^1.94)	Find the Derivative - d/dt 699/((t+1)^0.94)
d(cos(e^cos(t)))/d(t)	2sin(2e^cos(t))e^cos(t)sin(t)*cos(t)	Find the Derivative - d/dt cos(e^(cos(t)^2))^2
d()/d(t)*(860−326/√(,t))	163/(t√(,t))	Find the Derivative - d/dt 860-326/( square root of t)
d()/d(t)(ccos(t)+t^2*sin(t))	(2t−c)sin(t)+t^2*cos(t)	Find the Derivative - d/dt ccos(t)+t^2sin(t)
d()/d(t)cos((πt)/4)	−π/4sin((πt)/4)	Find the Derivative - d/dt cos((pit)/4)
d()/d(t)*(1/(t−3))^2	−2/((t−3)^3)	Find the Derivative - d/dt f(t)=(1/(t-3))^2
d()/d(t)(3ln(t))/(at−b*t^2)	(3a−3bt−3(a−2bt)ln(t))/((at−b*t^2)^2)	Find the Derivative - d/dt (3 natural log of t)/(at-bt^2)
d()/d(t)(t^2)/2	t	Find the Derivative - d/dt (t^2)/2
d()/d(t)*(t^2−3)	2*t	Find the Derivative - d/dt y=t^2-3
(d(6)*t^2)/d(t)	12*t	Find the Derivative - d/dt 6t^2
d()/d(x)(x^2−9)/(x−3)	1	Find the Derivative - d/dx (x^2-9)/(x-3)
d()/d(x)1/((1−2*x)^3)	6/((1−2*x)^4)	Find the Derivative - d/dx 1/((1-2x)^3)
d()/d(x)1/(4*x^2)	−1/(2*x^3)	Find the Derivative - d/dx 1/(4x^2)
d()/d(x)1/(x^(1/2))	−1/(2*x^(3/2))	Find the Derivative - d/dx 1/(x^(1/2))
d()/d(x)1/2*(e^x+e^(−x))	(e^x−e^(−x))/2	Find the Derivative - d/dx 1/2*(e^x+e^(-x))
d()/d(x)3/(x^4)	−12/(x^5)	Find the Derivative - d/dx 3/(x^4)
d()/d(x)(2x+5)/(3x−2)	−19/((3*x−2)^2)	Find the Derivative - d/dx (2x+5)/(3x-2)
d()/d(x)5x^(3/2)	(15*x^(1/2))/2	Find the Derivative - d/dx 5x^(3/2)
d()/d(x)2/(x+3)	−2/((x+3)^2)	Find the Derivative - d/dx 2/(x+3)
d(5*x+2)/d(x)	50*x+20	Find the Derivative - d/dx (5x+2)^2
d(2*x−1)/d(x)	8*x−4	Find the Derivative - d/dx (2x-1)^2
d()/d(x)(2*x−1)/(x^2)	(2−2*x)/(x^3)	Find the Derivative - d/dx (2x-1)/(x^2)
x^3−3*x	see full solution →	Find the Local Maxima and Minima x^3-3x
d()/d(x)(7x−x^2)	7 - 2x	Find the Derivative - d/dx y=7x-x^2
d()/d(x)(x^2−4)/(x−2)	1	Find the Derivative - d/dx (x^2-4)/(x-2)
d()/d(x)3^(xln(x))	3^(xln(x))ln(3)*(1+ln(x))	Find the Derivative - d/dx 3^(x natural log of x)
d()/d(x)(4−sec(x))/tan(x)	(cos(x)−4)/sin^2(x)	Find the Derivative - d/dx (4-sec(x))/(tan(x))
d()/d(x)(x^2+6x)	2*x+6	Find the Derivative - d/dx x^2+6x
d(e^(r*x))/d(x)	re^(rx)	Find the Derivative - d/dx e^(rx)
d()/d(x)sin(tan(4x))	4sec^2(4x)cos(tan(4x))	Find the Derivative - d/dx y=sin(tan(4x))
d(√(,x^2+7))/d(x)	x/√(,x^2+7)	Find the Derivative - d/dx square root of x^2+7
d()/d(x)(x−2)(2*x+3)	4*x−1	Find the Derivative - d/dx (x-2)(2x+3)
d()/d(x)*(x/4−4/x)	1/4+4/(x^2)	Find the Derivative - d/dx x/4-4/x
d(√(,x^2+21))/d(x)	x/√(,x^2+21)	Find the Derivative - d/dx square root of x^2+21
d()/d(x)(x^2)/cos(x)	(2xcos(x)+x^2*sin(x))/cos^2(x)	Find the Derivative - d/dx (x^2)/(cos(x))
d()/d(x)ln(x^2)/x	(2−ln(x^2))/(x^2)	Find the Derivative - d/dx ( natural log of x^2)/x
d(e^(7√(,x)))/d(x)	(7*e^(7√(,x)))/(2√(,x))	Find the Derivative - d/dx e^(7 square root of x)
d()/d(x)ln(x)/(8*x)	(1−ln(x))/(8*x^2)	Find the Derivative - d/dx ( natural log of x)/(8x)
d()/d(x)ln(x)/(x^6)	(1−6*ln(x))/(x^7)	Find the Derivative - d/dx ( natural log of x)/(x^6)
d()/d(x)ln(x)/(e^x)	(1−xln(x))/(xe^x)	Find the Derivative - d/dx ( natural log of x)/(e^x)
d(sin(√(,cos(tan(π*x)))))/d(x)	see full solution →	Find the Derivative - d/dx sin( square root of cos(tan(pix)))
d()/d(x)*π^5	0	Find the Derivative - d/dx y=pi^5
d(√(,ln(3*x)))/d(x)	1/(2x√(,ln(3x)))	Find the Derivative - d/dx square root of natural log of 3x
d(√(,8*x))/d(x)	2/√(,2*x)	Find the Derivative - d/dx square root of 8x
d()/d(x)cos(x)/x	(−x*sin(x)−cos(x))/(x^2)	Find the Derivative - d/dx (cos(x))/x
d(√(,3*x−2))/d(x)	3/(2√(,3*x−2))	Find the Derivative - d/dx square root of 3x-2
d()/d(x)(x^5)/(x^3)	2*x	Find the Derivative - d/dx (x^5)/(x^3)
d()/d(x)sin(tan(2x))	2sec^2(2x)cos(tan(2x))	Find the Derivative - d/dx y=sin(tan(2x))
d()/d(x)1/(x^7)	−7/(x^8)	Find the Derivative - d/dx y=1/(x^7)
d()/d(x)(9√(,x)+8)x^2	45/2x^(3/2)+16x	Find the Derivative - d/dx y=(9 square root of x+8)x^2
d()/d(x)x/10	1/10	Find the Derivative - d/dx x/10
d()/d(x)(2x^3sin(x)−3x*cos(x))	2x^3cos(x)+6x^2sin(x)+3xsin(x)−3*cos(x)	Find the Derivative - d/dx 2x^3sin(x)-3xcos(x)
(d(2)xcos(x))/d(x)	2cos(x)−2x*sin(x)	Find the Derivative - d/dx 2xcos(x)
d()/d(x)2x^(1/2)	1/√(,x)	Find the Derivative - d/dx 2x^(1/2)
d()/d(x)(2x+2*y)	2+2d(y)/d(x)	Find the Derivative - d/dx 2x+2y
d()/d(x)(3*x^2)/7	(6*x)/7	Find the Derivative - d/dx (3x^2)/7
d()/d(x)3x^2*y^2	6xy^2+6x^2yd(y)/d(x)	Find the Derivative - d/dx 3x^2y^2
d()/d(x)3/(2*x)	−3/(2*x^2)	Find the Derivative - d/dx 3/(2x)
d()/d(x)3x*ln(x)	3+3*ln(x)	Find the Derivative - d/dx 3x natural log of x
d()/d(x)(x^5)/10	(x^4)/2	Find the Derivative - d/dx (x^5)/10
d()/d(x)x^6e^x	x^5e^x(x+6)	Find the Derivative - d/dx y=x^6e^x
(d(3)sin(3x))/d(x)	9cos(3x)	Find the Derivative - d/dx 3sin(3x)
d()/d(x)(3x−4)	3	Find the Derivative - d/dx 3x-4
(d(5)e^(−4x))/d(x)	−20e^(−4x)	Find the Derivative - d/dx 5e^(-4x)
d()/d(x)4sin(x)*cos(x)	4cos(2x)	Find the Derivative - d/dx 4sin(x)cos(x)
(d(4)*sec(x))/d(x)	4sec(x)tan(x)	Find the Derivative - d/dx 4sec(x)
d()/d(x)*(sin(x)/(1+cos(x)))^2	(2*sin(x))/((1+cos(x))^2)	Find the Derivative - d/dx ((sin(x))/(1+cos(x)))^2
d()/d(x)5arctan(x)	5/(1+x^2)	Find the Derivative - d/dx 5arctan(x)
d()/d(x)xe^(x*y)	e^(xy)(x^2d(y)/d(x)+x*y+1)	Find the Derivative - d/dx xe^(xy)
d()/d(x)(x^3−3x)	3*x^2−3	Find the Derivative - d/dx x^3-3x
d()/d(x)x^8ln(x)	x^7(1+8ln(x))	Find the Derivative - d/dx x^8 natural log of x
d(x^(7*x))/d(x)	7x^(7x)*(1+ln(x))	Find the Derivative - d/dx x^(7x)
d(x^(8*x))/d(x)	8x^(8x)*(ln(x)+1)	Find the Derivative - d/dx x^(8x)
d()/d(x)(x^3−3/2x^2)	3x^2−3x	Find the Derivative - d/dx x^3-3/2x^2
d()/d(x)x^2ln(5*x)	x(1+2ln(5*x))	Find the Derivative - d/dx x^2 natural log of 5x
d()/d(x)x^2arctan(x)	(x^2)/(1+x^2)+2xarctan(x)	Find the Derivative - d/dx x^2arctan(x)
d()/d(x)*5	0	Find the Derivative - d/dx 5
d()/d(x)(1/2x−1/3)	1/2	Find the Derivative - d/d@VAR f(x)=1/2x-1/3
(lim_x→8)((x^2−64)/(x−8))	16	Evaluate the Limit
d()/d(x)*(−9/x)	9/(x^2)	Find the Derivative - d/d@VAR f(x)=-9/x
d()/d(x)(4x^4+7x^3−3x^2−4x+5)/(x^3)	4+3/(x^2)+8/(x^3)−15/(x^4)	Find the Derivative - d/d@VAR f(x)=(4x^4+7x^3-3x^2-4x+5)/(x^3)
d()/d(x)*(x^2+x−6)	2*x+1	Find the Derivative - d/d@VAR f(x)=x^2+x-6
d()/d(x)(2x^2+1)	4*x	Find the Derivative - d/d@VAR f(x)=2x^2+1
d()/d(x)√(,1−4*x)	−2/√(,1−4*x)	Find the Derivative - d/d@VAR f(x) = square root of 1-4x
d()/d(x)*(−8/x)	8/(x^2)	Find the Derivative - d/d@VAR f(x)=-8/x
(d(2)tan(3x))/d(x)	6sec^2(3x)	Find the Derivative - d/dx 2tan(3x)
d^2()/(d(x)^2)(x^2−1)/(x^2+1)	(4−12*x^2)/((x^2+1)^3)	Find the 2nd Derivative f(x)=(x^2-1)/(x^2+1)
d()/d(t)1/(3+t)	−1/((3+t)^2)	Find the Derivative - d/d@VAR f(t)=1/(3+t)
arcsec(2)	π/3	Evaluate arcsec(2)
d()/d(x)9/(x^2)	−18/(x^3)	Find the Derivative - d/d@VAR f(x)=9/(x^2)
ƒ(x)=x^4−24x^2+12x	see full solution →	Find the Concavity f(x)=x^4-24x^2+12x
(d(sec(θ))*tan(θ))/d(θ)	sec^3(θ)+sec(θ)*tan^2(θ)	Find the Derivative - d/dx sec(theta)tan(theta)
d(sin(θ))/d(θ)	cos(θ)	Find the Derivative - d/dx sin(theta)
d()/d(x)(x^3−3x^2+1)	3x^2−6x	Find the Derivative - d/d@VAR f(x)=x^3-3x^2+1
d()/d(x)d()/d(x)	d^2()/(d(x)^2)	Find the Derivative - d/dd d/(dx)
d()/d(r)4/3πr^2	8/3πr	Find the Derivative - d/dr 4/3*(pr^2)
d()/d(r)r/√(,r^2+1)	1/((r^2+1)^(3/2))	Find the Derivative - d/dr y=r/( square root of r^2+1)
(d(2)*cos(t))/d(t)	−2*sin(t)	Find the Derivative - d/dt 2cos(t)
d()/d(s())s()/(1+s^2())	(1−s^2())/((1+s^2)^2)	Find the Derivative - d/ds s/(1+s^2)
d()/d(s())A(s)=d()/d(s())(−12/s^5())	60/s^6()	Find the Derivative - d/ds A(s)=-12/(s^5)
(x+h)^4	x^4+4x^3h+6x^2h^2+4xh^3+h^4	Multiply (x+h)^4
(2+h)^3	8+12h+6h^2+h^3	Multiply (2+h)^3
(x^2−2x−8)/(x^3+x^2−2x)	(x−4)/(x^2−x)	Simplify (x^2-2x-8)/(x^3+x^2-2x)
√(,sin(x))	√(,sin(x))	Simplify square root of sin(x)
arccot(1/√(,3))	π/3	Simplify arccot(1/( square root of 3))
√(,√(3,1−x))	√(6,1−x)	Simplify square root of cube root of 1-x
7cos(x)sin(y)=3	tan(x)*tan(y)	Find dy/dx 7cos(x)*sin(y)=3
ƒ(x)=sin(e^(−x))	Domain: *(−∞,∞)	Find the Domain f(x)=sin(e^(-x))
domain of *arcsin(e^x)	Domain: *(−∞,0]	Find the Domain arcsin(e^x)
arcsec(2/√(,3))	π/6	Simplify arcsec(2/( square root of 3))
(√(3,y))^2	√(3,y^2)	Simplify ( cube root of y)^2
d()/d(x)*(−x/y)	(xd(y)/d(x)−y)/(y^2)	Find the Derivative Using Quotient Rule - d/dx -x/y
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative Using Product Rule - d/dx sec(x)
d(sec(x))/d(x)	sec(x)*tan(x)	Find the Derivative Using Chain Rule - d/dx sec(x)
7cos(xy)=3x+8y	−(8+7xsin(xy))/(7ysin(xy)+3)	Find dx/dy 7cos(xy)=3x+8y
d(x)/d(t)* for x=4t^2+t	8*t+1	Find dx/dt x=4t^2+t
(lim_x→0)((3*(1−cos(x)))/x)	0	Evaluate the Limit
(∫_^)(1/(x^4)*d(x))	−1/(3*x^3)+C	Find the Integral 1/(x^4)
( \int	x	,dx )
(∫_^)(4/x*d(x))	$4 \ln	x
(∫_^)(4xd(x))	2*x^2+C	Find the Integral 4x
(∫_^)(x^7*d(x))	(x^8)/8+C	Find the Integral x^7
(∫_^)(x^(3/2)*d(x))	(2*x^(5/2))/5+C	Find the Integral x^(3/2)
d()/d(x)xsin(2/x)	see full solution →	Find the Derivative - d/dx y=xsin(2/x)
d()/d(x)(x/3.1+3.1/x)(x^2+1)	(3*x^2+1)/3.1+3.1−3.1/(x^2)	Find the Derivative - d/dx (x/3.1+3.1/x)(x^2+1)
d(sin(tan(x)))/d(x)	cos(tan(x))*sec^2(x)	Find the Derivative - d/dx y=sin(tan(x))
d(sin(9*x))/d(x)	9cos(9x)	Find the Derivative - d/dx y=sin(9x)
y=x^2+5	5	Find the Horizontal Tangent Line y=x^2+5
d()/d(x)(6√(,x)+5cos(x))	3/√(,x)−5*sin(x)	Find the Derivative - d/dx 6 square root of x+5cos(x)
(d(x)*e^(y/z))/d(y)	(x*e^(y/z))/z	Find the Derivative - d/dy xe^(y/z)
d()/d(y)4y	4	Find the Derivative - d/dy 4y
(∫_^)(√(,x)*d(x))	2/3*x^(3/2)+C	Find the Integral square root of x
d(y^(1/2))/d(y)	1/(2√(,y))	Find the Derivative - d/dy y^(1/2)
(d(2)*y^3)/d(y)	6*y^2	Find the Derivative - d/dy 2y^3
d()/d(y)(y−3)/(y^2−3*y+9)	(−y^2+6y)/((y^2−3y+9)^2)	Find the Derivative - d/dy (y-3)/(y^2-3y+9)
d(ln(y^2))/d(y)	2/y	Find the Derivative - d/dy natural log of y^2
d(√(3,z))/d(z)	1/(3√(3,z^2))	Find the Derivative - d/dz cube root of z
d(√(5,7*x))/d(x)	7/(5√(5,2401*x^4))	Find the Derivative - d/dx fifth root of 7x
d()/d(x)4e^x	4*e^x	Find the Derivative - d/dx y=4e^x
d()/d(x)(3x−1)	3	Find the Derivative - d/dx y=3x-1
d()/d(x)(5x^2+cos(x))	10*x−sin(x)	Find the Derivative - d/dx y=5x^2+cos(x)
d()/d(x)(5xe^x−5e^x)	5xe^x	Find the Derivative - d/dx y=5xe^x-5e^x
d()/d(x)2sin(x)*cos(x)	2cos(2x)	Find the Derivative - d/dx y=2sin(x)cos(x)
d()/d(x)(3x^2+4*x)	6*x+4	Find the Derivative - d/dx y=3x^2+4x
d()/d(x)3e^(5*x)	15e^(5x)	Find the Derivative - d/dx y=3e^(5x)
d()/d(x)*(16−x^4)	−4*x^3	Find the Derivative - d/dx y=16-x^4
d()/d(x)5x*arcsin(x)	(5x)/√(,1−x^2)+5arcsin(x)	Find the Derivative - d/dx y=5xarcsin(x)
d()/d(x)6x^3*e^(−x)	6x^2e^(−x)*(3−x)	Find the Derivative - d/dx y=6x^3e^(-x)
d()/d(x)7arctan(x−√(,1+x^2))	7/(2*(1+x^2))	Find the Derivative - d/dx y=7arctan(x- square root of 1+x^2)
d(cos(8*x))/d(x)	−8sin(8x)	Find the Derivative - d/dx cos(8x)
d()/d(x)πcos(6*x+0.71)	−6πsin(6*x+0.71)	Find the Derivative - d/dx y=picos(6x+0.71)
d()/d(x)*ln(tan(x))	2csc(2x)	Find the Derivative - d/dx y = natural log of tan(x)
d()/d(x)x^5cos(x)	5x^4cos(x)−x^5*sin(x)	Find the Derivative - d/dx x^5cos(x)
d()/d(x)*ln(x^5)	5/x	Find the Derivative - d/dx y = natural log of x^5
d()/d(x)*ln(x^6)	6/x	Find the Derivative - d/dx y = natural log of x^6
d()/d(x)*ln(x/(1+x^2))	(1−x^2)/(x*(1+x^2))	Find the Derivative - d/dx y = natural log of x/(1+x^2)
d()/d(x)(3x^2−9x+11)/(2*x+4)	(3x^2+12x−29)/(2*(x+2)^2)	Find the Derivative - d/dx (3x^2-9x+11)/(2x+4)
d()/d(x)*(sin(x))^ln(x)	(sin(x))^ln(x)(ln(sin(x))/x+ln(x)cot(x))	Find the Derivative - d/dx y=(sin(x))^( natural log of x)
d()/d(x)*ln(10/x)	−1/x	Find the Derivative - d/dx y = natural log of 10/x
d()/d(x)(7−sec(x))/tan(x)	(sec(x)−7*sec^2(x))/tan^2(x)	Find the Derivative - d/dx y=(7-sec(x))/(tan(x))
d()/d(x)e^(−16x)	−16e^(−16x)	Find the Derivative - d/dx y=e^(-16x)
d()/d(x)*e^(1/x)	−(e^(1/x))/(x^2)	Find the Derivative - d/dx y=e^(1/x)
d()/d(x)*arccos(x^2)	−(2*x)/√(,1−x^4)	Find the Derivative - d/dx y=arccos(x^2)
d()/d(x)(x^2−6x)	2*x−6	Find the Derivative - d/dx x^2-6x
d()/d(x)*e^cos(x)	−sin(x)*e^cos(x)	Find the Derivative - d/dx y=e^(cos(x))
d()/d(x)*(2−x^2)	−2*x	Find the Derivative - d/dx 2-x^2
d()/d(x)(x/3.4+3.4/x)(x^2+1)	(3*x^2+1)/3.4+3.4−3.4/(x^2)	Find the Derivative - d/dx (x/3.4+3.4/x)(x^2+1)
d()/d(x)ln((x^4+5x^2)^(3/2))	(6x^2+15)/(x^3+5x)	Find the Derivative - d/dx y = natural log of (x^4+5x^2)^(3/2)
d()/d(x)7/(6*x^2)	−7/(3*x^3)	Find the Derivative - d/dx 7/(6x^2)
d()/d(x)*tan^2(x)	2tan(x)sec^2(x)	Find the Derivative - d/dx y=tan(x)^2
d()/d(x)x^2sin(8*x)	8x^2cos(8x)+2xsin(8x)	Find the Derivative - d/dx y=x^2sin(8x)
d()/d(x)x^2ln(6*x)	x(1+2ln(6*x))	Find the Derivative - d/dx y=x^2 natural log of 6x
d(ln(x^8))/d(x)	8/x	Find the Derivative - d/dx natural log of x^8
d()/d(x)*((x+5)/(x^2+2))^2	(2(x+5)(−x^2−10*x+2))/((x^2+2)^3)	Find the Derivative - d/dx ((x+5)/(x^2+2))^2
d()/d(x)x^2ln(2*x)	x+2xln(2*x)	Find the Derivative - d/dx y=x^2 natural log of 2x
d()/d(x)(x^3−3x)	3*x^2−3	Find the Derivative - d/dx y=x^3-3x
d()/d(x)(x^3−4x)	3*x^2−4	Find the Derivative - d/dx y=x^3-4x
d()/d(x)*x^tan(x)	x^tan(x)(sec^2(x)ln(x)+tan(x)/x)	Find the Derivative - d/dx y=x^(tan(x))
d()/d(x)(x^3−3x^2+1)	3x^2−6x	Find the Derivative - d/dx y=x^3-3x^2+1
d()/d(x)x/(x^2+81)	(81−x^2)/((x^2+81)^2)	Find the Derivative - d/dx x/(x^2+81)
d()/d(x)(4x−3*x^2)	$4 - 6x$	Find the Derivative - d/dx 4x-3x^2
d()/d(x)(x^3−3x^2+10x−5)/(x^2)	1−10/(x^2)+10/(x^3)	Find the Derivative - d/dx (x^3-3x^2+10x-5)/(x^2)
d()/d(x)*((x^5)/10−16/(x^2))	(x^4)/2+32/(x^3)	Find the Derivative - d/dx (x^5)/10-16/(x^2)
d()/d(x)*x^(−2/5)	−2/5*x^(−7/5)	Find the Derivative - d/dx y=x^(-2/5)
d(arctan(4*x))/d(x)	4/(1+16*x^2)	Find the Derivative - d/dx arctan(4x)
d()/d(x)x/(2−tan(x))	(2−tan(x)+x*sec^2(x))/((2−tan(x))^2)	Find the Derivative - d/dx y=x/(2-tan(x))
d()/d(x)*x^(1/3)	1/(3*x^(2/3))	Find the Derivative - d/dx y=x^(1/3)
d()/d(x)√(,x−4)/√(,x+4)	4/((x+4)√(,x^2−16))	Find the Derivative - d/dx
d()/d(x)*(√(,x)−1/√(,x))	1/(2√(,x))+1/(2*x√(,x))	Find the Derivative - d/dx
d()/d(x)√(,sin(√(,x)))	cos(√(,x))/(4√(,x)√(,sin(√(,x))))	Find the Derivative - d/dx
d()/d(x)√(,5−7*x)	−7/(2√(,5−7*x))	Find the Derivative - d/dx y = square root of 5-7x
d()/d(x)√(,ln(2*x))	1/(2x√(,ln(2x)))	Find the Derivative - d/dx y = square root of natural log of 2x
d()/d(x)√(,3−7*x)	−7/(2√(,3−7*x))	Find the Derivative - d/dx y = square root of 3-7x
(d(5)*x^5)/d(x)	25*x^4	Find the Derivative - d/dx 5x^5
d()/d(x)(x^2−6*x+12)/(x−4)	(x^2−8*x+12)/((x−4)^2)	Find the Derivative - d/dx y=(x^2-6x+12)/(x-4)
d()/d(x)1/(x^6)	−6/(x^7)	Find the Derivative - d/dx y=1/(x^6)
d()/d(x)1/(1+x^2)	−(2*x)/((1+x^2)^2)	Find the Derivative - d/dx y=1/(1+x^2)
d()/d(x)1/ln(x)	−1/(x*(ln(x))^2)	Find the Derivative - d/dx y=1/( natural log of x)
d()/d(x)4/√(,x)	−2/(x√(,x))	Find the Derivative - d/dx y=4/( square root of x)
d()/d(x)(5/((2x)^3)+2*cos(x))	−15/(8x^4)−2sin(x)	Find the Derivative - d/dx y=5/((2x)^3)+2cos(x)
d()/d(x)*29^x	29^x*ln(29)	Find the Derivative - d/dx y=29^x
d()/d(x)*23^x	23^x*ln(23)	Find the Derivative - d/dx y=23^x
d()/d(x)(3x^5−7x^2−4)/(x^2)	9*x^2+8/(x^3)	Find the Derivative - d/dx y=(3x^5-7x^2-4)/(x^2)
d()/d(x)(x^2+2x−2)/(x^2−2x+2)	(−4x^2+8x)/((x^2−2*x+2)^2)	Find the Derivative - d/dx y=(x^2+2x-2)/(x^2-2x+2)
d()/d(x)(−(x^2)/16+2/x−x^(3/2)+1/(3x^2)+x/3)	see full solution →	Find the Derivative - d/dx y=-(x^2)/16+2/x-x^(3/2)+1/(3x^2)+x/3
d()/d(x)(4x−1)^3	12(4x−1)^2	Find the Derivative - d/dx y=(4x-1)^3
d()/d(x)h(x)=ƒ(g(x))	ƒ^′(g(x))g(x)^′	Find the Derivative - d/dx h(x)=f(g(x))
d()/d(x)(x^2+5)/(x^2+6*x)	(6x^2−10x−30)/(x^2*(x+6)^2)	Find the Derivative - d/dx g(x)=(x^2+5)/(x^2+6x)
d(ln(x^2+100))/d(x)	(2*x)/(x^2+100)	Find the Derivative - d/dx natural log of x^2+100
d(ln(x/4))/d(x)	1/x	Find the Derivative - d/dx natural log of x/4
d(ln(x^2+25))/d(x)	(2*x)/(x^2+25)	Find the Derivative - d/dx natural log of x^2+25
d(ln(x^2−4*x))/d(x)	(2x−4)/(x^2−4x)	Find the Derivative - d/dx natural log of x^2-4x
d(ln(2*x+1))/d(x)	2/(2*x+1)	Find the Derivative - d/dx natural log of 2x+1
d(ln(sin(x)))/d(x)	2*cot(x)	Find the Derivative - d/dx natural log of sin(x)^2
d()/d(x)cos((πx)/2)	−π/2sin((πx)/2)	Find the Derivative - d/dx f(x)=cos((pix)/2)
d(cos(ln(x)))/d(x)	−sin(ln(x))/x	Find the Derivative - d/dx f(x)=cos( natural log of x)
d()/d(x)*x√(,x+4)	(3*x+8)/(2√(,x+4))	Find the Derivative - d/dx f(x)=x square root of x+4
d()/d(x)x√(,2x−3)	(3x−3)/√(,2x−3)	Find the Derivative - d/dx f(x)=x square root of 2x-3
d()/d(x)x(3*x−9)^3	3(3x−9)^2(4x−3)	Find the Derivative - d/dx f(x)=x(3x-9)^3
(d(sin(x))*tan(x))/d(x)	sin(x)*sec^2(x)+sin(x)	Find the Derivative - d/dx f(x)=sin(x)tan(x)
d()/d(x)5e^x√(,x)	5e^x√(,x)+(5e^x)/(2√(,x))	Find the Derivative - d/d@VAR g(x)=5e^x square root of x
d(sin(5*x))/d(x)	5cos(5x)	Find the Derivative - d/dx f(x)=sin(5x)
d()/d(x)*x√(,9−x)	(18−3*x)/(2√(,9−x))	Find the Derivative - d/dx x square root of 9-x
d()/d(x)xsin(3*x)	3xcos(3x)+sin(3x)	Find the Derivative - d/dx xsin(3x)
d()/d(x)xsin(x^2)	2x^2cos(x^2)+sin(x^2)	Find the Derivative - d/dx xsin(x^2)
d()/d(x)(7−x^2)(x^3−x+5)	−5x^4+24x^2−10*x−7	Find the Derivative - d/dx y=(7-x^2)(x^3-x+5)
d(tan(7*x))/d(x)	7sec^2(7x)	Find the Derivative - d/dx tan(7x)
d(tan(5*x^3))/d(x)	15x^2sec^2(5*x^3)	Find the Derivative - d/dx tan(5x^3)
d(tan(√(,1−x)))/d(x)	−sec^2(√(,1−x))/(2√(,1−x))	Find the Derivative - d/dx tan( square root of 1-x)
(d(sin(x))*cot(x))/d(x)	−sin(x)	Find the Derivative - d/dx sin(x)cot(x)
d(sin(9*ln(x)))/d(x)	(9cos(9ln(x)))/x	Find the Derivative - d/dx sin(9 natural log of x)
d()/d(x)(sin(2x)−2*sin(x))	2cos(2x)−2*cos(x)	Find the Derivative - d/dx sin(2x)-2sin(x)
d(sin(tan(7*x)))/d(x)	7cos(tan(7x))sec^2(7x)	Find the Derivative - d/dx sin(tan(7x))
d(sin(x^4))/d(x)	4x^3cos(x^4)	Find the Derivative - d/dx sin(x^4)
d()/d(x)x(1−2*x)^3	(1−2x)^2(1−8*x)	Find the Derivative - d/dx x(1-2x)^3
d()/d(x)x(6−2*x)^2	12(3−x)(1−x)	Find the Derivative - d/dx x(6-2x)^2
d()/d(x)xln(x)	1+ln(x)	Find the Derivative - d/dx x* natural log of x