Calculus — Full Problem Index (3/3)

d(ln(ln(8*x)))/d(x)

1/(x*ln(8*x))

Find the Derivative - d/dx natural log of natural log of 8x

d(ln(sin(3*x)))/d(x)

3*cot(3*x)

Find the Derivative - d/dx natural log of sin(3x)

d((log_)(5*x))/d(x)

1/(x*ln(10))

Find the Derivative - d/dx log of 5x

d()/d(x)(x^3−3*x^2+4)/(x^2)

1−8/(x^3)

Find the Derivative - d/dx f(x)=(x^3-3x^2+4)/(x^2)

d()/d(x)(1−x^2)/(1+x^2)

(−4*x)/((1+x^2)^2)

Find the Derivative - d/dx f(x)=(1-x^2)/(1+x^2)

d()/d(x)*(−1/2+7/5*x^3)

21/5*x^2

Find the Derivative - d/dx f(x)=-1/2+7/5x^3

d()/d(x)(x−1)/(x+1)

2/((x+1)^2)

Find the Derivative - d/dx y=(x-1)/(x+1)

d()/d(x)*6*x^(1/2)

3*x^(−1/2)

Find the Derivative - d/dx 6x^(1/2)

(d(7)*cos(x))/d(x)

−7*sin(x)

Find the Derivative - d/dx 7cos(x)

d()/d(x)*8*x*(x^2+9)^3

8*(x^2+9)^2*(7*x^2+9)

Find the Derivative - d/dx 8x(x^2+9)^3

d()/d(x)*8√(,x)

4/√(,x)

Find the Derivative - d/dx 8 square root of x

d(arctan(3*x))/d(x)

3/(1+9*x^2)

Find the Derivative - d/dx arctan(3x)

d(arctan(sin(x)))/d(x)

cos(x)/(1+sin^2(x))

Find the Derivative - d/dx arctan(sin(x))

d()/d(x)*9*x*y

9*xd(y)/d(x)+9*y

Find the Derivative - d/dx 9xy

d(cos(√(,x)))/d(x)

−sin(√(,x))/(2√(,x))

Find the Derivative - d/dx cos( square root of x)

d(cos(1/x))/d(x)

sin(1/x)/(x^2)

Find the Derivative - d/dx cos(1/x)

(d(a)*x)/d(x)

a

Find the Derivative - d/dx ax

d(cos(2*arctan(x)))/d(x)

−(4*x)/((1+x^2)^2)

Find the Derivative - d/dx cos(2arctan(x))

d(csc(3*x))/d(x)

−3*csc(3*x)*cot(3*x)

Find the Derivative - d/dx csc(3x)

d(csc(h(x)))/d(x)

−csc(h(x))*cot(h(x))*h(x)^′

Find the Derivative - d/dx csc(h(x))

(d(−)*cot(x))/d(x)

csc^2(x)

Find the Derivative - d/dx -cot(x)

d()/d(x)*(2*x^2−3*x)

4*x−3

Find the Derivative - d/dx f(x)=2x^2-3x

d()/d(x)*2√(,x)

1/√(,x)

Find the Derivative - d/dx f(x)=2 square root of x

d()/d(x)*(x^3−12*x)

3*x^2−12

Find the Derivative - d/dx f(x)=x^3-12x

d(x^9)/d(x)

9*x^8

Find the Derivative - d/dx f(x)=x^9

d()/d(x)*(2*cos(x)+sin(2*x))

−2*sin(x)+2*cos(2*x)

Find the Derivative - d/dx f(x)=2cos(x)+sin(2x)

d()/d(x)*(−3*x√(,x+1))

(−3*(3*x+2))/(2√(,x+1))

Find the Derivative - d/dx f(x)=-3x square root of x+1

d()/d(x)*5*x^3

15*x^2

Find the Derivative - d/dx f(x)=5x^3

d()/d(x)*x^9*e^x

x^8*e^x*(x+9)

Find dy/dx y=x^9e^x

d()/d(x)*e^cos(x)

−sin(x)*e^cos(x)

Find the Derivative - d/dx f(x)=e^(cos(x))

d(e^sin(x))/d(x)

e^sin(x)*cos(x)

Find the Derivative - d/dx f(x)=e^(sin(x))

d()/d(x)7/√(,x)

−7/(2*x√(,x))

Find the Derivative - d/dx f(x)=7/( square root of x)

d()/d(x)*(log_5)(x*e^x)

(1+x)/(x*ln(5))

Find the Derivative - d/dx f(x) = log base 5 of xe^x

d()/d(t)1/(1+t)

−1/((1+t)^2)

Find the Derivative - d/d@VAR f(t)=1/(1+t)

d()/d(x)*(x^2−16/x)

2*x+16/(x^2)

Find the Derivative - d/d@VAR f(x)=x^2-16/x

ƒ(x)=cos(x)

arccos(x)

Find the Inverse f(x)=cos(x)

ƒ(x)=1+√(,2+3*x)

((x−1)^2−2)/3,x≥1

Find the Inverse f(x)=1+ square root of 2+3x

d()/d(t)*4*t^(−1/8)

−1/2*t^(−9/8)

Find the Derivative - d/d@VAR g(t)=4t^(-1/8)

d()/d(x)*(2^9⋅0)

0

Find the Derivative - d/d@VAR f(x)=2^9*0

d()/d(x)*(√(,x)+5/√(,x))

1/(2√(,x))−5/(2*x√(,x))

Find the Derivative - d/d@VAR

d()/d(x)*(log_5)(x*e^x)

(1+x)/(x*ln(5))

Find the Derivative - d/d@VAR f(x) = log base 5 of xe^x

d()/d(x)*e^(−2*x)

−2*e^(−2*x)

Find the Derivative - d/d@VAR f(x)=e^(-2x)

d()/d(x)8/x

−8/(x^2)

Find the Derivative - d/d@VAR f(x)=8/x

d()/d(x)√(,3−2*x)

−1/√(,3−2*x)

Find the Derivative - d/d@VAR f(x) = square root of 3-2x

d(x^11)/d(x)

11*x^10

Find the Derivative - d/d@VAR f(x)=x^11

d()/d(x)x/(x^2−1)

−(x^2+1)/((x^2−1)^2)

Find the Derivative - d/d@VAR f(x)=x/(x^2-1)

d()/d(x)9/x

−9/(x^2)

Find the Derivative - d/d@VAR f(x)=9/x

d()/d(x)*x^2*e^x

x^2*e^x+2*x*e^x

Find the Derivative - d/d@VAR f(x)=x^2e^x

d()/d(x)*x^(5/2)*e^x

x^(3/2)*e^x*(x+5/2)

Find the Derivative - d/d@VAR f(x)=x^(5/2)e^x

d()/d(x)*(x^2*ln(x^2))

2*x*(1+2*ln(x))

Find the Derivative - d/d@VAR f(x)=x^2 natural log of x^2

d()/d(x)*(x^5−3*x^4)

5*x^4−12*x^3

Find the Derivative - d/d@VAR f(x)=x^5-3x^4

d()/d(x)*5*x^4

20*x^3

Find the Derivative - d/d@VAR f(x)=5x^4

−30*x^4+120*x^3

−30*x^3*(x−4)

Factor -30x^4+120x^3

−3*x^2+18*x+120

−3*(x−10)*(x+4)

Factor -3x^2+18x+120

−3*x^2+24*x+60

−3*(x−10)*(x+2)

Factor -3x^2+24x+60

12*x^2−24*x

12*x*(x−2)

Factor 12x^2-24x

12*x^2+6*x−6

$6(2x - 1)(x + 1)$

Factor 12x^2+6x-6

u^4−1

(u−1)*(u+1)*(u^2+1)

Factor u^4-1

u^3−64

(u−4)*(u^2+4*u+16)

Factor u^3-64

(∫_^)(3*x*d(x))

(3*x^2)/2+C

Find the Integral 3x

(∫_^)(3^x*d(x))

3^x/ln(3)+C

Find the Integral 3^x

(∫_^)(e^(4*x)*d(x))

(e^(4*x))/4+C

Find the Integral e^(4x)

x^3<49*x

x^3<49*x⇒(−∞,−7)∪(0,7)

Convert to Interval Notation x^3<49x

(∫_^)(sec(x)*tan(x)*d(x))

sec(x)+C

Find the Integral sec(x)tan(x)

√(,x+y)=1+x^2*y^2

(4*x*y^2√(,x+y)−1)/(1−4*x^2*y√(,x+y))

Find dy/dx square root of x+y=1+x^2y^2

√(,x*y)=x^2*y+1

(4*x*y√(,x*y)−y)/(x−2*x^2√(,x*y))

Find dy/dx square root of xy=x^2y+1

√(,x*y)=4+x^2*y

(4*x*y√(,x*y)−y)/(x−2*x^2√(,x*y))

Find dy/dx square root of xy=4+x^2y

e^y*sin(x)=x+x*y

(1+y−e^y*cos(x))/(e^y*sin(x)−x)

Find dy/dx e^ysin(x)=x+xy

(∫_^)(x*e^x*d(x))

x*e^x−e^x+C

Find the Antiderivative xe^x

x^2*y^2−x*y=8

(y−2*x*y^2)/(2*x^2*y−x)

Find dy/dx x^2y^2-xy=8

(∫_^)(ln(x)*d(x))

x*ln(x)−x+C

Find the Integral natural log of x

x*e^y=y−1

(e^y)/(1−x*e^y)

Find dy/dx xe^y=y-1

y^4=y^2−x^2

(−x)/(2*y^3−y)

Find dy/dx y^4=y^2-x^2

d^2()/(d(x)^2)*(3*x^3+7)^7

126*x*(3*x^3+7)^5*(30*x^3+7)

Find the 2nd Derivative f(x)=(3x^3+7)^7

x*sin(y)=y*cos(x)

(y*sin(x)+sin(y))/(cos(x)−x*cos(y))

Find dy/dx xsin(y)=ycos(x)

x*y=8

−y/x

Find dy/dx xy=8

d()/d(x)*8√(,x)

4/√(,x)

Find the Derivative - d/dx y=8 square root of x

cos(x*y^2)=y

−(y^2*sin(x*y^2))/(1+2*x*y*sin(x*y^2))

Find dy/dx cos(xy^2)=y

cos(x*y)+x^7=y^7

(7*x^6−y*sin(x*y))/(7*y^6+x*sin(x*y))

Find dy/dx cos(xy)+x^7=y^7

4*x+5*y=x*y

(y−4)/(5−x)

Find dy/dx 4x+5y=xy

d()/d(x)*12√(,x)

6/√(,x)

Find the Derivative - d/dx y=12 square root of x

d()/d(x)*x^8*e^x

x^8*e^x+8*x^7*e^x

Find dy/dx y=x^8e^x

d()/d(t)*(11*t−t^2)^(2/3)

(22−4*t)/(3√(3,11*t−t^2))

Find ds/dt s=(11t-t^2)^(2/3)

d(A)/d(p)* where *A=p*r^2

r^2

Find dA/dp A=pr^2

(d(θ)*cos(θ)*sin(θ))/d(θ)

θ*cos(2*θ)+1/2*sin(2*θ)

Find the Derivative - d/dx thetacos(theta)sin(theta)

4*x^2−y^2=5

(4*x)/y

Find dy/dx 4x^2-y^2=5

4*x^2+x*y+4*y^2=9

−(8*x+y)/(x+8*y)

Find dy/dx 4x^2+xy+4y^2=9

4*x^2−y^2=3

(4*x)/y

Find dy/dx 4x^2-y^2=3

3*y^2=(2*x−5)/(2*x+5)

10/(3*y*(2*x+5)^2)

Find dy/dx 3y^2=(2x-5)/(2x+5)

3*(x^2+y^2)^2=100*(x^2−y^2)

(50*x−3*x*(x^2+y^2))/(3*y*(x^2+y^2)+50*y)

Find dy/dx 3(x^2+y^2)^2=100(x^2-y^2)

(∫_^)(√(,7)*d(x))

√(,7)*x+C

Evaluate the Integral

(∑_n=1^∞)(−)*4*(−1/2)^(n−1)

$1}^{\infty} -4\left(-\frac{1}{2}\right)^{n-1} = -\frac{8}{3}$

Evaluate the Summation

2*x^2+y^2=54

−(2*x)/y

Find dy/dx 2x^2+y^2=54

x*e^y−10*x+3*y=0

(10−e^y)/(x*e^y+3)

Find dy/dx xe^y-10x+3y=0

x*y^4+x^2*y=x+3*y

(1−y^4−2*x*y)/(4*x*y^3+x^2−3)

Find dy/dx xy^4+x^2y=x+3y

x^3+y^3=9*x*y

(3*y−x^2)/(y^2−3*x)

Find dy/dx x^3+y^3=9xy

x^3+y^3=28

−(x^2)/(y^2)

Find dy/dx x^3+y^3=28

(∫_^)(x*sin(x)*d(x))

−x*cos(x)+sin(x)+C

Evaluate the Integral integral of xsin(x) with respect to x

d()/d(x)*(x^2−6)

2*x

Find the Derivative - d/d@VAR f(x)=x^2-6

x^2*y^3−2*x*y^2=5

(2*y^2−2*x*y^3)/(3*x^2*y^2−4*x*y)

Find dy/dx x^2y^3-2xy^2=5

(lim_x→3)((x^2+3*x−18)/(x^2−9))

3/2

Evaluate the Limit

(x*y+1)^3=x−y^2+8

(1−3*y*(x*y+1)^2)/(3*x*(x*y+1)^2+2*y)

Find dy/dx (xy+1)^3=x-y^2+8

d()/d(t)*(4−t)

−1

Find dy/dt y=4-t

d()/d(t)*(5−t)

−1

Find dy/dt y=5-t

(10−x)*y^2=x^3

(3*x^2+y^2)/(2*y*(10−x))

Find dy/dx (10-x)y^2=x^3

d()/d(x)*(x^(−2)+x)^(−3)

(6*x^(−3)−3)/((x^(−2)+x)^4)

Find dy/dx y=(x^-2+x)^-3

sin(x*y)=x^2−y

(2*x−y*cos(x*y))/(x*cos(x*y)+1)

Find dy/dx sin(xy)=x^2-y

y=√(,x−2)/√(,x+2)

2/((x−2)^(1/2)*(x+2)^(3/2))

Find dy/dx

x*cos(y)+y*cos(x)=1

(y*sin(x)−cos(y))/(cos(x)−x*sin(y))

Find dy/dx xcos(y)+ycos(x)=1

y+16*x*y−12=0

−(16*y)/(1+16*x)

Find dy/dx y+16xy-12=0

4*x*y=32

−y/x

Find dy/dx 4xy=32

d()/d(x)√(,5−9*x)

−9/(2√(,5−9*x))

Find dy/dx y = square root of 5-9x

d()/d(x)x/(2−tan(x))

(2−tan(x)+x*sec^2(x))/((2−tan(x))^2)

Find dy/dx y=x/(2-tan(x))

d()/d(x)*x^2*sin(8*x)

8*x^2*cos(8*x)+2*x*sin(8*x)

Find dy/dx y=x^2sin(8x)

d()/d(x)*(x*ln(x))

1+ln(x)

Find dy/dx y=x natural log of x

y*cos(x)=5*x^2+2*y^2

(10*x+y*sin(x))/(cos(x)−4*y)

Find dy/dx ycos(x)=5x^2+2y^2

x^3+y^3=6*x*y−1

(2*y−x^2)/(y^2−2*x)

Find dy/dx x^3+y^3=6xy-1

d()/d(x)*e^(2*x)

2*e^(2*x)

Find the Derivative - d/dx y=e^(2x)

d()/d(x)*4*x^7

28*x^6

Find the Derivative - d/dx y=4x^7

d()/d(x)*3√(,x)

3/(2√(,x))

Find the Derivative - d/dx y=3 square root of x

d()/d(x)*x^ln(x)

2*ln(x)*x^(ln(x)−1)

Find the Derivative - d/dx y=x^( natural log of x)

d()/d(x)*(16*x^(1/2)+4*x)

8/√(,x)+4

Find the Derivative - d/dx y=16x^(1/2)+4x

d()/d(x)*ln(4*x)

1/x

Find the Derivative - d/dx y = natural log of 4x

d()/d(x)*ln(cos(x))

−tan(x)

Find the Derivative - d/dx y = natural log of cos(x)

d()/d(x)*sin(x)*cos(x)

cos(2*x)

Find the Derivative - d/dx y=sin(x)cos(x)

d()/d(x)*(8*x^3+7)^(3/2)

36*x^2√(,8*x^3+7)

Find the Derivative - d/dx y=(8x^3+7)^(3/2)

d()/d(x)1/(x^4)

−4/(x^5)

Find the Derivative - d/dx y=1/(x^4)

d()/d(x)*4^(e^(x^2))

2*x*ln(4)*e^(x^2)*4^(e^(x^2))

Find the Derivative - d/dx y=4^(e^(x^2))

d()/d(x)cot(x)/(1+cot(x))

(−csc^2(x))/((1+cot(x))^2)

Find dy/dx y=(cot(x))/(1+cot(x))

d()/d(x)*x*e^x

e^x*(x+1)

Find dy/dx y=xe^x

d()/d(x)*(x√(,1−x^2))

(1−2*x^2)/√(,1−x^2)

Find dy/dx y=x square root of 1-x^2

ƒ(x)=(x^2−100)/((x−9)*(x+3))

9,x=−3; Horizontal Asymptote: *y=1

Find the Asymptotes f(x)=(x^2-100)/((x-9)(x+3))

d(5^(3*x))/d(x)

3⋅5^(3*x)*ln(5)

Find the Derivative - d/dx 5^(3x)

d()/d(x)7/x

−7/(x^2)

Find the Derivative - d/dx 7/x

d()/d(x)1/tan(x)

−csc^2(x)

Find the Derivative - d/dx 1/(tan(x))

d(3^(2*x))/d(x)

2⋅3^(2*x)*ln(3)

Find the Derivative - d/dx 3^(2x)

(d(p)*r^2)/d(r)

2*p*r

Find the Derivative - d/dr pr^2

(d(−)*2*x)/d(x)

−2

Find the Derivative - d/dx -2x

d(arctan(x/2))/d(x)

2/(4+x^2)

Find the Derivative - d/dx arctan(x/2)

d(cos(sin(x)))/d(x)

−sin(sin(x))*cos(x)

Find the Derivative - d/dx cos(sin(x))

d(csc(2*x))/d(x)

−2*csc(2*x)*cot(2*x)

Find the Derivative - d/dx csc(2x)

(d(6)*sec(x))/d(x)

6*sec(x)*tan(x)

Find the Derivative - d/dx 6sec(x)

(d(6)*x)/d(x)

6

Find the Derivative - d/dx 6x

d()/d(x)*7*x

7

Find the Derivative - d/dx 7x

d^2()/(d(x)^2)*(10*x^9*y^5+7*x^4*y^8)

720*x^7*y^5+84*x^2*y^8

Find the 2nd Derivative 10x^9y^5+7x^4y^8

d^2()/(d(x)^2)*12*x*(x^2+10)^5

120*x*(x^2+10)^3*(11*x^2+30)

Find the 2nd Derivative 12x(x^2+10)^5

(∑_i=1^24)(4)*i

$1}^{24} 4i = 1200$

Evaluate the Summation sum from i=1 to 24 of 4i

(∑_i=5^5)(5)

$5}^{5} 5 = 5$

Evaluate the Summation sum from 5 to 5 of 5

(∑_k=5^20)(26+4*k)

$5}^{20} (26 + 4k) = 1216$

Evaluate the Summation sum from k=5 to 20 of 26+4k

(∑_n=1^4)(2*n+1)

$1}^{4} (2n+1) = 24$

Evaluate the Summation sum from n=1 to 4 of 2n+1

(lim_x→8)(ln(√(,x))/(x^2))

(3*ln(2))/128

Evaluate Using L'Hospital's Rule

(lim_x→0^+)(x^sin(x))

1

Evaluate Using L'Hospital's Rule limit as x approaches 0 of x^(sin(x))

(lim_x→∞)(1−5/x)

e^(−5)

Evaluate Using L'Hospital's Rule limit as x approaches 8 of (1-5/x)^x

(∫_^)((y−1)^7*d(y))

((y−1)^8)/8+C

Evaluate the Integral integral of (y-1)^7 with respect to y

(∫_^)((arcsin(x))^2*d(x))

x*(arcsin(x))^2+2√(,1−x^2)*arcsin(x)−2*x+C

Evaluate the Integral

(∫_^)((e^arctan(x))/(1+x^2)*d(x))

e^arctan(x)+C

Evaluate the Integral

(∫_^)(ln(x)/x*d(x))

ln(x)/8+C

Evaluate the Integral

(∫_^)(sec^2(1/x)/(x^2)*d(x))

−tan(1/x)+C

Evaluate the Integral

(∫_^)(sec^2(x)/√(,tan(x))*d(x))

2√(,tan(x))+C

Evaluate the Integral

(∫_^)((e^x)/√(,1−e^(2*x))*d(x))

arcsin(e^x)+C

Evaluate the Integral

(∫_^)(((ln(x))^9)/x*d(x))

((ln(x))^10)/10+C

Evaluate the Integral

(∫_^)((x−1)√(,x)*d(x))

2/5*x^(5/2)−2/3*x^(3/2)+C

Evaluate the Integral

(∫_^)((x^6−3*x^2)^4*(x^5−x)*d(x))

((x^6−3*x^2)^5)/30+C

Evaluate the Integral

(∫_^)((x^4+9)^8*d(x))

see full solution →

Evaluate the Integral integral of (x^4+9)^8 with respect to x

(∫_^)(√(,t^6+7*t)*(6*t^5+7)*d(t))

2/3*(t^6+7*t)^(3/2)+C

Evaluate the Integral

(∫_^)((x^3−2*x^2)*(1/x−5)*d(x))

−5/4*x^4+11/3*x^3−x^2+C

Evaluate the Integral

d^4()/(d(x)^4)*(10*x^3+9*x^2)

0

Find the 4th Derivative y=10x^3+9x^2

(∫_^)(4*x^3−3/(x^3)*d(x))

x^4+3/(2*x^2)+C

Evaluate the Integral

(∫_^)((1−6*x)*e^(3*x−9*x^2)*d(x))

(e^(3*x−9*x^2))/3+C

Evaluate the Integral

(∫_^)(2*x−3*x^2*d(x))

x^2−x^3+C

Evaluate the Integral integral of 2x-3x^2 with respect to x

(∫_^)(2*sin(x)+3*cos(x)*d(x))

−2*cos(x)+3*sin(x)+C

Evaluate the Integral

d^2()/(d(x)^2)*(x^2+8)^9

18*(x^2+8)^7*(17*x^2+8)

Find the 2nd Derivative f(x)=(x^2+8)^9

d^2(cos(2*x))/(d(x)^2)

−4*cos(2*x)

Find the 2nd Derivative cos(2x)

d^2()/(d(x)^2)*(2*sin(x)+sin(2*x))

−2*sin(x)−4*sin(2*x)

Find the 2nd Derivative 2sin(x)+sin(2x)

ƒ(x)=x*e^(−x^2)

2*x*e^(−x^2)*(2*x^2−3)

Find the 2nd Derivative f(x)=xe^(-x^2)

ƒ(x)=cos(x)

−cos(x)

Find the 2nd Derivative f(x)=cos(x)

y=12

0

Find the 2nd Derivative y=12

d^2()/(d(x)^2)*x*e^x

e^x*(x+2)

Find the 2nd Derivative y=xe^x

d^2(sin(2*x))/(d(x)^2)

−4*sin(2*x)

Find the 2nd Derivative sin(2x)

d^2(sec(x−π/2))/(d(x)^2)

csc(x)*(cot^2(x)+csc^2(x))

Find the 2nd Derivative sec(x-pi/2)

d^3()/(d(x)^3)*(4*x^3+5*x^2)

24

Find the 3rd Derivative y=4x^3+5x^2

d^3(sin(x))/(d(x)^3)

−cos(x)

Find the 3rd Derivative y=sin(x)

(∫_^)(5/(9*x^2+49)*d(x))

5/21*arctan((3*x)/7)+C

Evaluate the Integral

d()/d(x)*20√(,x)

10/√(,x)

Find the Derivative - d/dx y=20 square root of x

d^3()/(d(x)^3)1/x

−6/(x^4)

Find the 3rd Derivative f(x)=1/x

(∫_^)(1/(4*x^3)*d(x))

−1/(8*x^2)+C

Evaluate the Integral integral of 1/(4x^3) with respect to x

(∫_^)(1/(6*x^5)*d(x))

−1/(24*x^4)+C

Evaluate the Integral integral of 1/(6x^5) with respect to x

(∫_^)(1/(x*(ln(x))^4)*d(x))

−1/(3*(ln(x))^3)+C

Evaluate the Integral

(∫_^)(1/(x√(,9*x^2−1))*d(x))

$\text{sec}^{-1}(

3x

(∫_^)(1/(x−3)*d(x))

$\ln

x-3

(∫_^)(1/(7*x+3)*d(x))

$\frac{1}{7} \ln

7x+3

(∫_^)(1/(6*x+4)*d(x))

$\frac{1}{6} \ln

6x+4

(∫_^)(1/(7*x^6)*d(x))

−1/(35*x^5)+C

Evaluate the Integral integral of 1/(7x^6) with respect to x

(∫_^)(1/(7*x^3)*d(x))

−1/(14*x^2)+C

Evaluate the Integral integral of 1/(7x^3) with respect to x

(∫_^)(1/(12*x^6)*d(x))

−1/(60*x^5)+C

Evaluate the Integral integral of 1/(12x^6) with respect to x

(∫_^)(1/(1+y^2)*d(y))

arctan(y)+C

Evaluate the Integral integral of 1/(1+y^2) with respect to y

(∫_^)(1/(x^8)*d(x))

−1/(7*x^7)+C

Evaluate the Integral integral of 1/(x^8) with respect to x

(∫_^)(1/(x^2−2*x)*d(x))

$\frac{1}{2} \ln\left

\frac{x - 2}{x} \right

(∫_^)(1/(x^2+16)*d(x))

1/4*arctan(x/4)+C

Evaluate the Integral integral of 1/(x^2+16) with respect to x

(∫_^)(1/(e^(2*x))*d(x))

−1/(2*e^(2*x))+C

Evaluate the Integral integral of 1/(e^(2x)) with respect to x

(∫_^)(1/(√(,x)*(1−√(,x)))*d(x))

$-2 \ln

1 - \sqrt{x}

(∫_^)(sec^2(x)/tan(x)*d(x))

$\ln

\tan(x)

(∫_^)((x^2−1)/(x^3+x)*d(x))

$\ln\left

\frac{x^2+1}{x} \right

(∫_^)((x^2−1)/(x^3−3*x+1)*d(x))

$\frac{1}{3} \ln

x^3 - 3x + 1

(∫_^)((x^2−3*x+2)/(x+1)*d(x))

$\frac{x^2}{2} - 4x + 6 \ln

x + 1

(∫_^)((x^2−4)/x*d(x))

$\frac{x^2}{2} - 4 \ln

x

(∫_^)((z^2)/√(3,1+z^3)*d(z))

1/2*(1+z^3)^(2/3)+C

Evaluate the Integral

(∫_^)(1/((x−2)^(3/2))*d(x))

−2/√(,x−2)+C

Evaluate the Integral

(∫_^)(4/(x^3+4*x)*d(x))

$\ln

x

(∫_^)(−5/r*d(r))

$-5 \ln

r

(∫_^)(5/(x^2+1)*d(x))

5*arctan(x)+C

Evaluate the Integral integral of 5/(x^2+1) with respect to x

(∫_^)(5/(x^3)*d(x))

−5/(2*x^2)+C

Evaluate the Integral integral of 5/(x^3) with respect to x

(∫_^)(cos(x)/x*d(x))

Ci(x)+C

Evaluate the Integral integral of (cos(x))/x with respect to x

(∫_^)(cos(π/x)/(x^2)*d(x))

−sin(π/x)/π+C

Evaluate the Integral

(lim_x→2)(√(,(2*x^3+4)/(x^2+1)))

2

Evaluate the Limit

(∫_^)(19/(2+5*y)*d(y))

$\frac{19}{5} \ln

2+5y

(∫_^)(2/(x^2−1)*d(x))

$\ln\left

\frac{x-1}{x+1} \right

(∫_^)(3/(x*ln(x))*d(x))

$3 \ln

\ln(x)

(∫_^)(34/(x^2)*d(x))

−34/x+C

Evaluate the Integral integral of 34/(x^2) with respect to x

(∫_^)((3*x^2−4)/(x^2)*d(x))

3*x+4/x+C

Evaluate the Integral

(∫_π/6^π)(sin(x)*d(x))

(2+√(,3))/2

Evaluate the Integral

(∫_^)(sin^4(x)*cos(x)*d(x))

sin^5(x)/5+C

Evaluate the Integral

(∫_^)(sec^5(x)*d(x))

see full solution →

Evaluate the Integral integral of sec(x)^5 with respect to x

(∫_^)(sec^2(x)*tan^3(x)*d(x))

tan^4(x)/4+C

Evaluate the Integral

(∫_^)(sec^2(x)*tan^5(x)*d(x))

tan^6(x)/6+C

Evaluate the Integral

(∫_^)(sec^2(x)−sin(x)*d(x))

tan(x)+cos(x)+C

Evaluate the Integral

(∫_^)(sec^2(4*x)*d(x))

1/4*tan(4*x)+C

Evaluate the Integral integral of sec(4x)^2 with respect to x

(∫_^)(sin(2*x)*cos(2*x)*d(x))

sin(2*x)/12+C

Evaluate the Integral

(∫_^)(sin^6(x)*d(x))

see full solution →

Evaluate the Integral integral of sin(x)^6 with respect to x

(∫_^)(sin(x)*cos(x)*d(x))

cos(x)/8−cos(x)/6+C

Evaluate the Integral

(∫_^)(tan(x)*sec(x)*d(x))

tan(x)/4+C

Evaluate the Integral

(∫_^)(1/(2*x+1)*d(x))

$\frac{1}{2} \ln

2x+1

(∫_^)(cos(4*x)*d(x))

sin(4*x)/4−sin(4*x)/12+C

Evaluate the Integral integral of cos(4x)^3 with respect to x

(∫_^)(e^(−x^4)*(−4*x^3)*d(x))

e^(−x^4)+C

Evaluate the Integral

(∫_^)(e^(2*x)*sin(2*x)*d(x))

(e^(2*x)*(sin(2*x)−cos(2*x)))/4+C

Evaluate the Integral

(∫_^)(e^(1−x)*d(x))

−e^(1−x)+C

Evaluate the Integral integral of e^(1-x) with respect to x

(∫_^)(ln(x^6)/x*d(x))

3*(ln(x))^2+C

Evaluate the Integral

(∫_^)(e^x*x*d(x))

e^x*(x−1)+C

Evaluate the Integral integral of e^xx with respect to x

(∫_^)(ln(x)/(2*x)*d(x))

((ln(x))^2)/4+C

Evaluate the Integral

(∫_^)(ln(2*x)/x*d(x))

((ln(2*x))^2)/2+C

Evaluate the Integral

(∫_^)(8*x*d(x))

4*x^2+C

Evaluate the Integral integral of 8x with respect to x

(∫_π/3^π)(sin(x)*d(x))

3/2

Evaluate the Integral

(∫_^)(e^(7*x+4)*d(x))

(e^(7*x+4))/7+C

Evaluate the Integral integral of e^(7x+4) with respect to x

(∫_^)(e^(−8*x)*d(x))

−1/8*e^(−8*x)+C

Evaluate the Integral integral of e^(-8x) with respect to x

(∫_^)(e^(3*x)*cos(4*x)*d(x))

(3*e^(3*x)*cos(4*x)+4*e^(3*x)*sin(4*x))/25+C

Evaluate the Integral

(∫_^)(x/√(,x+4)*d(x))

2/3*(x+4)^(3/2)−8√(,x+4)+C

Evaluate the Integral

(∫_^)(x/(x^4+2*x^2+1)*d(x))

−1/(2*(x^2+1))+C

Evaluate the Integral

(∫_^)(x/(1+4*x^2)*d(x))

1/8*ln(1+4*x^2)+C

Evaluate the Integral integral of x/(1+4x^2) with respect to x

(∫_^)(x^2*cos(x)*d(x))

x^2*sin(x)+2*x*cos(x)−2*sin(x)+C

Evaluate the Integral integral of x^2*cos(x) with respect to x

(∫_^)(x^2*e^(7*x)*d(x))

(e^(7*x))/7*(x^2−(2*x)/7+2/49)+C

Evaluate the Integral integral of x^2e^(7x) with respect to x

(∫_^)(x^2−5*x+4*d(x))

(x^3)/3−(5*x^2)/2+4*x+C

Evaluate the Integral integral of x^2-5x+4 with respect to x

(∫_^)(x^2*e^(8*x)*d(x))

(e^(8*x))/8*(x^2−x/4+1/32)+C

Evaluate the Integral integral of x^2e^(8x) with respect to x

(∫_^)(x^2*e^(9*x)*d(x))

see full solution →

Evaluate the Integral integral of x^2e^(9x) with respect to x

(∫_^)(√(5,x^3)*d(x))

5/8*x^(8/5)+C

Evaluate the Integral

(∫_^)(√(9,x)*d(x))

9/10*x^(10/9)+C

Evaluate the Integral

(∫_^)(√(3,x)*(x−4)*d(x))

3/7*x^(7/3)−3*x^(4/3)+C

Evaluate the Integral

(∫_^)(√(,x)*ln(2*x)*d(x))

2/3*x^(3/2)*ln(2*x)−4/9*x^(3/2)+C

Evaluate the Integral

(∫_^)(√(,y)*d(y))

2/3*y^(3/2)+C

Evaluate the Integral

(∫_^)(√(,4*x+5)*d(x))

1/6*(4*x+5)^(3/2)+C

Evaluate the Integral

(∫_^)(√(,4*x−1)*d(x))

1/6*(4*x−1)^(3/2)+C

Evaluate the Integral

(∫_^)(√(,8*x+3)*d(x))

1/12*(8*x+3)^(3/2)+C

Evaluate the Integral

(∫_^)(x^2*sin(x^3)*d(x))

−1/3*cos(x^3)+C

Evaluate the Integral

(∫_^)(x^2*ln(x)*d(x))

(x^3*ln(x))/3−(x^3)/9+C

Evaluate the Integral

(∫_^)(x^3*cos(2*x)*d(x))

see full solution →

Evaluate the Integral integral of x^3cos(2x) with respect to x

(∫_^)(x^7*ln(x)*d(x))

(x^8*ln(x))/8−(x^8)/64+C

Evaluate the Integral

(∫_0^π/2)(cos((2*x)/3)*d(x))

(3√(,3))/4

Evaluate the Integral

(∫_0^π/2)(sin^5(x)*d(x))

8/15

Evaluate the Integral

(∫_0^π/2)(cos(x)*d(x))

8/15

Evaluate the Integral

(∫_^)(x*e^(x/3)*d(x))

3*x*e^(x/3)−9*e^(x/3)+C

Evaluate the Integral integral of xe^(x/3) with respect to x

(∫_^)(x*e^(8*x)*d(x))

1/8*x*e^(8*x)−1/64*e^(8*x)+C

Evaluate the Integral integral of xe^(8x) with respect to x

(∫_^)(y*e^y*d(y))

e^y*(y−1)+C

Evaluate the Integral integral of ye^y with respect to y

(∫_^)(3*e^(3*x)*d(x))

e^(3*x)+C

Evaluate the Integral integral of 3e^(3x) with respect to x

(∫_^)(3*x^2*e^(x^3)*d(x))

e^(x^3)+C

Evaluate the Integral

(∫_^)(3*x^3*d(x))

(3*x^4)/4+C

Evaluate the Integral integral of 3x^3 with respect to x

(∫_^)(3*x*e^(5*x)*d(x))

3/5*x*e^(5*x)−3/25*e^(5*x)+C

Evaluate the Integral integral of 3xe^(5x) with respect to x

(∫_^)(3*cos(x)*d(x))

3*sin(x)+C

Evaluate the Integral integral of 3cos(x) with respect to x

(∫_−4^2)(x^2+2*x−8*d(x))

−36

Evaluate the Integral

(∫_^)(2*sec^2(x)*d(x))

2*tan(x)+C

Evaluate the Integral integral of 2sec(x)^2 with respect to x

(∫_^)(2*sin^2(x)*d(x))

x−sin(2*x)/2+C

Evaluate the Integral integral of 2sin(x)^2 with respect to x

(∫_^)(2*e^(−3*x)*d(x))

−2/3*e^(−3*x)+C

Evaluate the Integral integral of 2e^(-3x) with respect to x

(∫_^)(2*(2*x+4)^5*d(x))

((2*x+4)^6)/6+C

Evaluate the Integral integral of 2(2x+4)^5 with respect to x

(∫_^)(2*cos^2(x)*d(x))

x+sin(2*x)/2+C

Evaluate the Integral integral of 2cos(x)^2 with respect to x

(∫_2^4)(x^2−6*x+9*d(x))

2/3

Evaluate the Integral

(∫_−3^−2)(2*x*(4−x^2)^3*d(x))

625/4

Evaluate the Integral

(∫_−3^2)(x^2+x−6*d(x))

−125/6

Evaluate the Integral

(∫_^)(2*ln(x)*d(x))

2*x*ln(x)−2*x+C

Evaluate the Integral

(∫_^)(20*t^3*e^(−t^4)*d(t))

−5*e^(−t^4)+C

Evaluate the Integral

(∫_24^25)(x√(,x^2−576)*d(x))

343/3

Evaluate the Integral

(∫_^)(−24*x^5*d(x))

−4*x^6+C

Evaluate the Integral integral of -24x^5 with respect to x

(∫_^)(25−x^2*d(x))

25*x−(x^3)/3+C

Evaluate the Integral integral of 25-x^2 with respect to x

(∫_^)(7*x^(−4)*d(x))

−7/(3*x^3)+C

Evaluate the Integral integral of 7x^-4 with respect to x

(∫_^)(7*x*e^(5*x^2)*d(x))

(7*e^(5*x^2))/10+C

Evaluate the Integral integral of 7xe^(5x^2) with respect to x

(∫_^)(−7*t^(−1)*d(t))

$-7\ln

t

(∫_−6^7)(x*d(x))

13/2

Evaluate the Integral

(∫_^)(6*x^3*d(x))

(3*x^4)/2+C

Evaluate the Integral integral of 6x^3 with respect to x

(∫_^)(5*sin(x)*d(x))

−5*cos(x)+C

Evaluate the Integral integral of 5sin(x) with respect to x

(∫_^)(5*x√(3,1−x^2)*d(x))

−15/8*(1−x^2)^(4/3)+C

Evaluate the Integral

(∫_^)(5*e^(−2*x)*d(x))

−5/2*e^(−2*x)+C

Evaluate the Integral integral of 5e^(-2x) with respect to x

(∫_4^9)(1/√(,x)*d(x))

2

Evaluate the Integral

(∫_^)(4*x^3*sin(x^4)*d(x))

−cos(x^4)+C

Evaluate the Integral

(∫_^)(4√(3,x^2)*d(x))

(12*x^(5/3))/5+C

Evaluate the Integral

ƒ(x)=√(,x),(1,1)

1/2*x+1/2

Find the Tangent Line at the Point square root of x , (1,1)

y^3=x^5

(5*x^4)/(3*y^2)

Find dy/dx y^3=x^5

(∫_^)((2*x)/√(,x^2+2*x+26)*d(x))

$2\sqrt{x^2+2x+26} - 2\ln

x+1 + \sqrt{x^2+2x+26}

(∫_^)(cot(x)*ln(sin(x))*d(x))

((ln(sin(x)))^2)/2+C

Evaluate the Integral

(∫_^)(csc(5*x)*d(x))

$-\frac{1}{5}\ln

\csc(5x) + \cot(5x)

(∫_^)(arctan(2*x)*d(x))

x*arctan(2*x)−1/4*ln(1+4*x^2)+C

Evaluate the Integral integral of arctan(2x) with respect to x

(∫_^)(arctan(4*x)*d(x))

x*arctan(4*x)−1/8*ln(1+16*x^2)+C

Evaluate the Integral integral of arctan(4x) with respect to x

(∫_^)(cos(√(,t))*d(t))

2√(,t)*sin(√(,t))+2*cos(√(,t))+C

Evaluate the Integral

(∫_^)(sin(x)*e^cos(x)*d(x))

−e^cos(x)+C

Evaluate the Integral

(∫_^)(sin(x)*cos(2*x)*d(x))

1/2*cos(x)−1/6*cos(3*x)+C

Evaluate the Integral

(∫_^)(x*sin(6*x)*d(x))

−x/6*cos(6*x)+1/36*sin(6*x)+C

Evaluate the Integral integral of xsin(6x) with respect to x

(∫_^)(x*sin(2*x^2)*d(x))

−1/4*cos(2*x^2)+C

Evaluate the Integral integral of xsin(2x^2) with respect to x

(∫_^)(x*sin(x/2)*d(x))

see full solution →

Evaluate the Integral integral of xsin(x/2) with respect to x

(∫_^)(t*sin(2*t)*d(t))

−t/2*cos(2*t)+1/4*sin(2*t)+C

Evaluate the Integral integral of tsin(2t) with respect to t

(∫_^)(x*(x−4)^9*d(x))

((x−4)^11)/11+(2*(x−4)^10)/5+C

Evaluate the Integral integral of x(x-4)^9 with respect to x

(∫_^)(x*(x+1)^8*d(x))

((x+1)^10)/10−((x+1)^9)/9+C

Evaluate the Integral integral of x(x+1)^8 with respect to x

(∫_^)(x*(8*x+7)^8*d(x))

((8*x+7)^10)/640−(7*(8*x+7)^9)/576+C

Evaluate the Integral integral of x(8x+7)^8 with respect to x

(∫_0^π/4)(7*sec(x)*tan(x)*d(x))

7√(,2)−7

Evaluate the Integral

(∫_0^π/4)(9*sec(x)*tan(x)*d(x))

9√(,2)−9

Evaluate the Integral

(∫_0^π/4)(sin(x)*d(x))

1−√(,2)/2

Evaluate the Integral

(∫_0^√(,3))((6*x)/√(,x^2+1)*d(x))

6

Evaluate the Integral

(∫_0^√(,π))(x*sin(x^2)*d(x))

1

Evaluate the Integral

(∫_0^1)(1/√(,1−x^2)*d(x))

π/2

Evaluate the Integral

(∫_0^1)((2*t−1)^2*d(t))

1/3

Evaluate the Integral

(∫_0^2)((1−4*x)^2*d(x))

86/3

Evaluate the Integral

(∫_0^8)(2*π*(0.5*x√(,1+(0.5)^2))*d(x))

16*π√(,5)

Evaluate the Integral

(∫_0^9)(ƒ(x)*d(x))

F(9)−F(0)

Evaluate the Integral

(∫_0^ln(2))(e^(2*x)*d(x))

3/2

Evaluate the Integral

(∫_0^ln(2))(x*e^x*d(x))

2*ln(2)−1

Evaluate the Integral

(∫_0^b)(9*x^8*d(x))

b^9

Evaluate the Integral

(∫_0^4)(ƒ(x)*d(x))

F(4)−F(0)

Evaluate the Integral

(∫_0^5)(4*x*d(x))

50

Evaluate the Integral

( \int_{0}^{5}

2x - 5

, dx )

(∫_0^2*π)(x*sin(x)*d(x))

−2*π

Evaluate the Integral

(∫_0^2)(8*x*e^(x^2)*d(x))

4*e^4−4

Evaluate the Integral

(∫_0^π)(x*cos(x)*d(x))

−2

Evaluate the Integral

(∫_−1^−1)(4*x−4*d(x))

0

Evaluate the Integral

(∫_−1^1)(x^100*d(x))

2/101

Evaluate the Integral

(∫_1^16)((x−3)/√(,x)*d(x))

24

Evaluate the Integral

(∫_1^2)(3*x^5−2*x^3*d(x))

24

Evaluate the Integral

(∫_1^3)(3*t^2+7*d(t))

40

Evaluate the Integral

(∫_2^5)(4−2*x*d(x))

−9

Evaluate the Integral

(∫_−2^−1)(2*x*(4−x^2)^3*d(x))

−81/4

Evaluate the Integral

(∫_−2^−1)((u−1)/(u^2)*d(u))

−1/2−ln(2)

Evaluate the Integral

(∫_^)(1−cos(x)*d(x))

x−sin(x)+C

Evaluate the Integral integral of 1-cos(x) with respect to x

(∫_^)(144−x^2*d(x))

144*x−(x^3)/3+C

Evaluate the Integral integral of 144-x^2 with respect to x

(∫_^)(14*x*d(x))

7*x^2+C

Evaluate the Integral integral of 14x with respect to x

(∫_^)(16*x*ln(2*x)*d(x))

8*x^2*ln(2*x)−4*x^2+C

Evaluate the Integral

(∫_^)(16*d(x))

16*x+C

Evaluate the Integral integral of 16 with respect to x

(∫_1^e)(1/x*d(x))

1

Evaluate the Integral

(∫_1^e)(x^2*ln(x)*d(x))

(2*e^3+1)/9

Evaluate the Integral

(∫_1^9)(9*x^2*d(x))

2184

Evaluate the Integral

(∫_^)(11*(11*x−7)^2*d(x))

((11*x−7)^3)/3+C

Evaluate the Integral

(∫_^)(10*x−3*d(x))

5*x^2−3*x+C

Evaluate the Integral integral of 10x-3 with respect to x

(∫_^)(−10*x^4*d(x))

−2*x^5+C

Evaluate the Integral integral of -10x^4 with respect to x

12/((2−3*(1/3))^3)

12

Evaluate 12/((2-3(1/3))^3)

24/4+12

18

Evaluate 24/4+12

−(3*(3)^2*(−7))/(2*(3)^3−(−7))

189/61

Evaluate -(3(3)^2(-7))/(2(3)^3-(-7))

d()/d(x)*(x^2+8)

2*x

Find the Derivative - d/d@VAR f(x)=x^2+8

d()/d(x)x/(x+1)

1/((x+1)^2)

Find the Derivative - d/d@VAR f(x)=x/(x+1)

(∫_^)(sin(3*x)*cos(5*x)*d(x))

cos(2*x)/4−cos(8*x)/16+C

Evaluate the Integral

d()/d(x)*8*x^3

24*x^2

Find the Derivative - d/d@VAR f(x)=8x^3

(lim_x→2)((x−2)/(x^3−8))

1/12

Evaluate the Limit limit as x approaches 2 of (x-2)/(x^3-8)

(√(,x−1))^2

x−1

Simplify ( square root of x-1)^2

d()/d(x)*(∫_^)(x*(2*x^2+3)^10*d(x))

x*(2*x^2+3)^10

Find the Derivative of the Integral

d()/d(x)*(∫_^)(sin(√(,x))/√(,x)*d(x))

sin(√(,x))/√(,x)

Find the Derivative of the Integral

d()/d(x)*(∫_^)(sin(2*x)/sin(x)*d(x))

2*cos(x)

Find the Derivative of the Integral

d()/d(x)*(∫_^)(cos(x)*d(x))

cos(x)

Find the Derivative of the Integral integral of cos(x)^5 with respect to x

d()/d(x)*(∫_0^6)(√(,36−x^2)*d(x))

0

Find the Derivative of the Integral

d()/d(x)*(∫_^)(x^3*d(x))

x^3

Find the Derivative of the Integral integral of x^3 with respect to x

(∫_^)(sin(x)*d(x))

−cos(x)+C

Find the Integral sin(x)

x^2+5*x+9*x*y−y^2=4

(−2*x−5−9*y)/(9*x−2*y)

Find dy/dx x^2+5x+9xy-y^2=4

(d(√(,x))*ln(x))/d(x)

(ln(x)+2)/(2√(,x))

Find the Derivative - d/dx square root of x natural log of x

(lim_t→∞)(√(,t+t^2)/(4*t−t^2))

0

Evaluate the Limit

(∫_^)((x−3)/(x^3)*d(x))

−1/x+3/(2*x^2)+C

Evaluate the Integral

d()/d(x)*6

0

Find the Derivative - d/dx 6

d(sin(x))/d(x)

sin(x)*(ln(sin(x))+x*cot(x))

Find the Derivative - d/dx sin(x)^x

y=(3*x−9)/(2*x+8)

42/((2*x+8)^2)

Find dy/dx y=(3x-9)/(2x+8)

x*y=6

−y/x

Find dy/dx xy=6

(lim_x→4)((x^2−16)/(x^2−5*x+4))

8/3

Evaluate the Limit

(∫_0^2)(ƒ(x)*d(x))

F(2)−F(0)

Evaluate the Integral

ƒ(x)=1/(x−1)

−1/((x−1)^2)

Use the Limit Definition to Find the Derivative f(x)=1/(x-1)

ƒ(x)=x^3

3*x^2

Use the Limit Definition to Find the Derivative f(x)=x^3

ƒ(x)=2/x

−2/(x^2)

Use the Limit Definition to Find the Derivative f(x)=2/x

d(x^3)/d(x)

3*x^2

Use the Limit Definition to Find the Derivative x^3

ƒ(x)=(x^2)/(x^2+3)

see full solution →

Find the Concavity f(x)=(x^2)/(x^2+3)

ƒ(x)=x^(1/3)*(x+4)

see full solution →

Find the Concavity f(x)=x^(1/3)(x+4)

y=6*x^4+8*x^3

see full solution →

Find the Inflection Points y=6x^4+8x^3

y=x−sin(x)

see full solution →

Find the Inflection Points y=x-sin(x)

ƒ(x)=x^4−6*x^2

see full solution →

Find the Concavity f(x)=x^4-6x^2

ƒ(x)=x^4−6*x^3+2*x+8

see full solution →

Find the Concavity f(x)=x^4-6x^3+2x+8

ƒ(x)=1/(x^2+7)

see full solution →

Find the Inflection Points f(x)=1/(x^2+7)

x^4−2*x^2

√(,3)/3,−√(,3)/3

Find the Inflection Points x^4-2x^2

x^4−4*x^3+10

(0,10),(2,−6)

Find the Inflection Points x^4-4x^3+10

ƒ(x)=−x^6+42*x^5−42*x+19

(0,19),(28,252104467)

Find the Inflection Points -x^6+42x^5-42x+19

ƒ(x)=(x^2)/(x^2+3)

(1,1/4),(−1,1/4)

Find the Inflection Points (x^2)/(x^2+3)

ƒ(x)=x^3+6*x^2+9*x

(−2,−2)

Find the Inflection Points f(x)=x^3+6x^2+9x

ƒ(x)=x/(4*x^2−1)

Inflection Point: *(0,0)

Find the Inflection Points f(x)=x/(4x^2-1)

ƒ(x)=x^4−4*x^3+5

(0,5),(2,−11)

Find the Inflection Points f(x)=x^4-4x^3+5

ƒ(x)=x^4−4*x^3+10

Inflection Points: *(0,10),(2,−6)

Find the Inflection Points f(x)=x^4-4x^3+10

ƒ(x)=3*x^4+4*x^3

see full solution →

Find the Inflection Points f(x)=3x^4+4x^3

ƒ(x)=4*x^3−12*x

(0,0)

Find the Inflection Points f(x)=4x^3-12x

y=−x^3+x^2+8*x+1

see full solution →

Find the Critical Points y=-x^3+x^2+8x+1

y=x^3−3*x^2−72*x

$6, -4$

Find the Critical Points y=x^3-3x^2-72x

y=x^3−4*x^2−16*x+5

see full solution →

Find the Critical Points y=x^3-4x^2-16x+5

g(x)=x^7−7*x^5

0,√(,5),−√(,5)

Find the Critical Points g(x)=x^7-7x^5

y=x*(x−2)

(1,−1)

Find the Critical Points y=x(x-2)

ƒ(x)=x^3−3*x+1

see full solution →

Find Where Increasing/Decreasing Using Derivatives f(x)=x^3-3x+1

ƒ(x)=x^3+18*x^2+2

Increasing on: *(−∞,−12)∪(0,∞)

Find Where Increasing/Decreasing Using Derivatives f(x)=x^3+18x^2+2

ƒ(x)=1/4*x^4−2*x^2

see full solution →

Find Where Increasing/Decreasing Using Derivatives f(x)=1/4x^4-2x^2

ƒ(x)=x^4−32*x^2

see full solution →

Find Where Increasing/Decreasing Using Derivatives f(x)=x^4-32x^2

ƒ(x)=x^4−4*x^3+10

see full solution →

Find Where Increasing/Decreasing Using Derivatives f(x)=x^4-4x^3+10

x=sec(1/y)

0⇒No solution

Find Where dy/dx is Equal to Zero x=sec(1/y)

((x−0)^2)/5^2+((y−0)^2)/3^2=1

see full solution →

Graph ((x-0)^2)/(5^2)+((y-0)^2)/(3^2)=1

y=x^2+3

3

Find the Horizontal Tangent Line y=x^2+3

y=2*x^3+3*x^2−12*x+1

$21, y = -6$

Find the Horizontal Tangent Line y=2x^3+3x^2-12x+1

y=2+8*x−x^2

18

Find the Horizontal Tangent Line y=2+8x-x^2

y=3*x^2+4*x

−4/3

Find the Horizontal Tangent Line y=3x^2+4x

d()/d(x)*6√(,x)

3/√(,x)

Find the Derivative - d/dx y=6 square root of x

x^2+y^2=14*x

$7, y = -7$

Find the Horizontal Tangent Line x^2+y^2=14x

ƒ(x)=x+5

see full solution →

Find the Domain and Range f(x)=x+5

ƒ(x)=ln(x−3)

Domain:(3,∞),Range:(−∞,∞)

Find the Domain and Range f(x) = natural log of x-3

ƒ(x)=(x−1)^2,(−5,3)

see full solution →

Determine if the Point is on the Graph f(x)=(x-1)^2 , (-5,3)

x^2*y^2−9*x^2−4*y^2=0

(9*x−x*y^2)/(x^2*y−4*y)

Find dy/dx x^2y^2-9x^2-4y^2=0

√(3,1.1)

√(3,1.1)≈1.0333

Evaluate cube root of 1.1

sin(−π/6)

−1/2

Evaluate sin(-pi/6)

−cos(π)

1

Evaluate -cos(pi)

sin(2*(0))

0

Evaluate sin(2(0))

cos(−1)

cos(1)

Evaluate cos(-1)

ƒ(x)=x^3−6*x^2+15

$0, 4$

Find the Critical Points f(x)=x^3-6x^2+15

ƒ(x)=x^2−4*x

2

Find the Critical Points f(x)=x^2-4x

(lim_t→−3)((t^2−9)/(2*t^2+7*t+3))

6/5

Evaluate the Limit

ƒ(x)=(x^2)/(x+1)

$0, x = -2$

Find the Critical Points f(x)=(x^2)/(x+1)

ƒ(x)=3*x^4+4*x^3

$0, -1$

Find the Critical Points f(x)=3x^4+4x^3

ƒ(x)=3*x^5−20*x^3

{−2,0,2}

Find the Critical Points f(x)=3x^5-20x^3

ƒ(x)=3*x^2+2*x^3

$0, -1$

Find the Critical Points f(x)=3x^2+2x^3

ƒ(x)=3*x^3−36*x

$2, -2$

Find the Critical Points f(x)=3x^3-36x

ƒ(x)=2*x^3−3*x^2−12*x+5

$2, -1$

Find the Critical Points f(x)=2x^3-3x^2-12x+5

ƒ(x)=2*x^3−24*x

−2,2

Find the Critical Points f(x)=2x^3-24x

500/3

166.*(6)

Evaluate 500/3

52/p

52/p

Evaluate 52/p

−csc(π/2)

−1

Evaluate -csc(pi/2)^2

ƒ(x)=(x+3)/(x^2+9)

see full solution →

Find Where Undefined/Discontinuous f(x)=(x+3)/(x^2+9)

ƒ(x)=x^2+5*x,x=4

13*x−16

Find the Tangent Line at x=4 f(x)=x^2+5x , x=4

ƒ(x)=x/(x−3)

x/(x−3)

Graph x/(x-3)

2*x^3−3*x^2−36*x+5

—

Graph 2x^3-3x^2-36x+5

4*x^2+y^2−8*x+4*y+4=0

1

Graph 4x^2+y^2-8x+4y+4=0

d()/d(θ)*sec(θ)*tan(θ)

sec^3(θ)+sec(θ)*tan^2(θ)

Find the Derivative - d/dx y=sec(theta)tan(theta)

ƒ(x)=ln(x^2+25)

ln(x^2+25)

Graph f(x) = natural log of x^2+25

ƒ(x)=sin(x)+cos(x)

√(,2)*sin(x+π/4)

Graph f(x)=sin(x)+cos(x)

ƒ(x)=x^3−12*x+1

—

Graph f(x)=x^3-12x+1

ƒ(x)=x/(x−1)

x/(x−1)

Graph f(x)=x/(x-1)

y=e^(−x^2)

e^(−x^2)

Graph y=e^(-x^2)

y=100−x^2,[−10,10]

y∈[0,100]

Solve over the Interval y=100-x^2 , [-10,10]

cos(2*x)+sin(x)=1,[0,2*π)

1⇒x=0,π/6,(5*π)/6,π

[Solve over the Interval cos(2x)+sin(x)=1 , 0,2pi)

ƒ(x)=(2*x^3−3*x−9)/(9*x^3−5*x^2+3)

2/9, Vertical Asymptote: *x≈−0.585

Find the Asymptotes f(x)=(2x^3-3x-9)/(9x^3-5x^2+3)

ƒ(x)=(2*x^2)/(x^2−16)

4,x=−4; Horizontal: *y=2

Find the Asymptotes f(x)=(2x^2)/(x^2-16)

ƒ(x)=(x^2+2*x−3)/(x^2+4*x−5)

−5, Horizontal Asymptote: *y=1

Find the Asymptotes f(x)=(x^2+2x-3)/(x^2+4x-5)

d()/d(x)*x^4

4*x^3

Find dy/dx y=x^4

d()/d(x)*x^cos(x)

x^cos(x)*(cos(x)/x−sin(x)*ln(x))

Find dy/dx y=x^(cos(x))

y=6*x−4*cos(3*x)

6+12*sin(3*x)

Find dy/dx y=6x-4cos(3x)

d()/d(x)*x^√(,x)

x^√(,x)(ln(x)+2)/(2√(,x))

Find dy/dx y=x^( square root of x)

y=x^2*y^3+x^3*y^2

(2*x*y^3+3*x^2*y^2)/(1−3*x^2*y^2−2*x^3*y)

Find dy/dx y=x^2y^3+x^3y^2

d()/d(x)*(x/3−3/x)

1/3+3/(x^2)

Find dy/dx y=x/3-3/x

d()/d(x)*3^x*x^3

3^x*x^2*(3+x*ln(3))

Find the Derivative - d/dx y=3^xx^3

d()/d(x)*(2*x−1)^4

8*(2*x−1)^3

Find the Derivative - d/dx y=(2x-1)^4

d()/d(x)*cos(x)

cos(x)*(ln(cos(x))−x*tan(x))

Find the Derivative - d/dx y=cos(x)^x

d()/d(x)(e^x)/(1−e^x)

(e^x)/((1−e^x)^2)

Find the Derivative - d/dx y=(e^x)/(1-e^x)

d()/d(x)*x√(3,x+1)

(4*x+3)/(3√(3,(x+1)^2))

Find the Derivative - d/dx y=x cube root of x+1

d()/d(x)*(log_)(x)

1/x

Find the Derivative - d/dx y = log of x

d()/d(x)*sec(x)*tan(x)

sec^3(x)+sec(x)*tan^2(x)

Find the Derivative - d/dx y=sec(x)tan(x)

d()/d(x)*ln(8*x)

1/x

Find the Derivative - d/dx y = natural log of 8x

d()/d(x)*ln(4*x^3−x^2)

(12*x−2)/(4*x^3−x^2)

Find the Derivative - d/dx y = natural log of 4x^3-x^2

d()/d(x)*cos(2*x)*sin(3*x)

3*cos(2*x)*cos(3*x)−2*sin(2*x)*sin(3*x)

Find the Derivative - d/dx y=cos(2x)sin(3x)

d()/d(x)*(−csc(x)−sin(x))

csc(x)*cot(x)−cos(x)

Find the Derivative - d/dy y=-csc(x)-sin(x)

d()/d(x)*(sin(x)/2+c/x)

cos(x)/2−c/(x^2)

Find the Derivative - d/dy y=(sin(x))/2+c/x

d()/d(x)*18√(,x)

9/√(,x)

Find the Derivative - d/dx y=18 square root of x

d()/d(x)*2√(,x)

1/√(,x)

Find the Derivative - d/dx y=2 square root of x

d()/d(x)*x^sin(x)

x^sin(x)*(sin(x)/x+cos(x)*ln(x))

Find the Derivative - d/dx y=x^(sin(x))

d()/d(x)*(5*x^3−4*x^2+3*x−6)

15*x^2−8*x+3

Find the Derivative - d/dx y=5x^3-4x^2+3x-6

d()/d(x)*(5*x^3−4*x)

15*x^2−4

Find the Derivative - d/dx y=5x^3-4x

d()/d(x)*(4*x^2−9*x)

8*x−9

Find the Derivative - d/dx y=4x^2-9x

d()/d(x)*(x^3−17*x^2+63*x+2)

3*x^2−34*x+63

Find the Derivative - d/dx y=x^3-17x^2+63x+2

d()/d(x)*(x^2−5*x)

2*x−5

Find the Derivative - d/dx y=x^2-5x

d()/d(x)*(x^2+3*x+2)

2*x+3

Find the Derivative - d/dx y=x^2+3x+2

d()/d(x)*(x^2*sin^4(x)+cos(x)^(−2))

4*x^2*sin^3(x)*cos(x)+2*x*sin^4(x)+2*sin(x)*sec^3(x)

Find the Derivative - d/dx y=x^2sin(x)^4+cos(x)^-2

d()/d(x)*x^12*e^x

x^11*e^x*(x+12)

Find the Derivative - d/dx y=x^12e^x

d()/d(x)*e^(7*x)/8

7/8*e^(7*x)/8

Find the Derivative - d/dx y=e^((7x)/8)

d()/d(x)ln(x)/(x^5)

(1−5*ln(x))/(x^6)

Find the Derivative - d/dx y=( natural log of x)/(x^5)

y*cos(x)=1+sin(x*y)

(y*cos(x*y)+y*sin(x))/(cos(x)−x*cos(x*y))

Find dy/dx ycos(x)=1+sin(xy)

d()/d(x)*sin(x)*cos(x)

cos(2*x)

Find dy/dx y=sin(x)cos(x)

d()/d(x)*(x^3+6*x^2)

3*x^2+12*x

Find dy/dx y=x^3+6x^2

y=−x/y

−1/(2*y)

Find dy/dx y=-x/y

d()/d(x)sin(x)/cos(x)

sec^2(x)

Find dy/dx y=(sin(x))/(cos(x))

d()/d(x)*(x+3)*(x^2−3)

3*x^2+6*x−3

Find dy/dx y=(x+3)(x^2-3)

(lim_x→2)(sin(x−2)/(x^2−4))

1/4

Evaluate the Limit

x*y=7

−y/x

Find dy/dx xy=7

3*x*y−x^2−4=0

(x^2+4)/(3*x)

Solve for y 3xy-x^2-4=0

x*y+y^2=1

−y/(x+2*y)

Find dy/dx xy+y^2=1

cos(x^2)=x*e^y

(−2*x*sin(x^2)−e^y)/(x*e^y)

Find dy/dx cos(x^2)=xe^y

cos(6*y)=x

−1/(6*sin(6*y))