Calculus Derivatives

Basic Derivatives

100

What is the derivative of

 y = 3x² ?

y' = 6x

200

Find the derivative of

 f(x) = ln6

f'(x)=0

300

Find the derivative of

 f(x) = 6x³ + x - 2

f'(x)=18x² + 1

400

Find the derivative of

 f(x) = 3sinx - 2cosx

f'(x)=3cosx + 2sinx

500

Find and SIMPLIFY f'(x):

f(x)=(3+x³-xe)/x

f'(x)=-3x^-2+2x

Product and Quotient Rule (and some mixed)

100

Find the derivative of

 y = 3x² sin x

y'=3x² cos x + 6x sin x

200

Find the derivative

f(x) = (3x - 2x²)(5 + 4x)

Do not simplify

f'(x)=(3x-2x²)(4)+(3-4x)4

300

Find the derivative of 

y = sin(5x )/(x² + 1)

Do not Simplify

y'=[(x²+1)cos(5x)5-sin(5x)2x]/(x²+1)²

400

Find the derivative of 

f(x) = (e^2xsin(x))/x⁴

f'(x)=[x⁴(e^2xcosx+2e^2xsinx)-e^2xsin(x)4x³]/(x⁴)²

500

The derivative of 

y=5ln(x³+7)tan(e^x)

y'= 5ln(x³+7)sec²(e^x)e^x+[5(3x²)tan(e^x)]/(x³+7)

Chain Rule

100

Find y' if 

y = (3x - 9)⁴

y'=12(3x - 9)³

200

Find the derivative of

 f(x) = sin (4x)

f'(x)=4 cos 4x

300

Find y' if 

y = (9x² + 4)^1/3

^{Do not simplify}

y'=1/3(9x²+4)^-2/318x

400

Find the derivative

f(x) = sin³(4x).

f'(x)=12sin²(4x) cos (4x)

500

The derivative

 f(x)=sec⁵(9^sin(x))

f'(x)=5sec⁴(9^sin(x))sec(9^sinx)tan(9^sinx)(ln9)(9^sinx)cosx

Trigonometric Derivatives

100

Find the derivative

f(x) = sec x

f'(x) = sec x tan x

200

Find the derivative

y = 3csc(2x)

y' = -6 csc(2x)cot(2x)

300

Find the derivative

 f(x) = sin x tan x

f'(x) = cos x tan x + sin x sec²x

400

Find the derivative of

 y = tan(sec x)

y' = sec x tan x sec ²(sec x)

500

Find the derivative of 

y=sin⁶(e^10x)

y'=6sin⁵(e^10x)cos(e^10x)e^10x10

Logarithmic and Exponential Derivatives

100

Find the second derivative of 

y = e^x. 

y'' = e^x

200

Find the derivative 

f(x) = ln(x²)

f'(x)=2/x

300

Find the derivative 

f(x) = 3^x2 

f'(x) = 2x ln3 3^x2

400

Find the derivative 

f(x) = ln(x/(x² + 1))

f'(x) = (1/x) - (2x/(x² + 1))

500

find the derivative

y = x^elog₃(x⁴+sin(x))

y'=x^e(4x³+cos(x))/(ln3(x⁴+sin(x)))+ex^elog₃(x⁴+sin(x))