AP Calculus Unit 2 & 3 Review: Differentiation

Basic DerivativeRules

100

Find the derivative of this function.

f(x)=3x²+6x+2

f'(x)=6x+6

200

Find the derivative of this function.

f(x)=2x^-10+7x^-2

f'(x)=-20x^-11-14x^-3

300

Find the derivative of this function.

f(x)=(3x-x²)(5+4x)

f'(x)=-24x²+4x+15

400

Find the derivative of this function.

f(x)=(x²+1)/x³

f'(x)=(2x³-3x⁴+3x²)/x⁶

500

Find the derivative of this function.

f(x)=(10x+1)/(x²+2)

f'(x)=(-10x²-2x+20)/(x²+2)²

Composite andInverse Functions

100

Find the derivative of this function.

f(x)=(3x+1)²

f'(x)=6(3x+1) OR f'(x)=18x+6

200

Find the derivative of this function.

f(x)=(4x-3)⁵

f'(x)=20(4x-3)⁴

300

Find the derivative of this function.

f(x)=3e^4x

f'(x)=12e^4x

400

If f(1)=-5, f(2)=-9, f'(1)=-2, f'(2)=1, g(1)=2, g(2)=4, and g is the inverse of f, find g'(1).

g'(1)=1

500

If f(2)=6, f(6)=8, f'(2)=1/3, f'(6)=3/2, and if g is the inverse of f, find g'(6).

g'(6)=3

Differentiation withTrig Functions

100

Find the derivative of this function.

f(x)=5sinx-4cosx

f'(x)=5cosx+4sinx

200

Find the derivative of this function.

f(x)=x³sin(5x)

f'(x)=3x²sin(5x)+5x³cos(5x)

300

Find the derivative of this function.

f(x)=cos(x)cot(x)

f'(x)=-csc(x)cot(x)-cos(x)

400

Find the derivative of this function.

f(x)=cos(2x)

f'(x)=-2sin(2x)

500

Find the derivative of this function.

f(x)=-3sin(4x²+5)

f'(x)=-24xcos(4x²+5)

Implicit Differentiation

100

Differentiate this function implicitly.

2x-y=-3

dy/dx=2

200

Differentiate this function implicitly.

x²+6x-8y+5y²=13

dy/dx=(x+3)/(4-5y)

300

Differentiate this function implicitly.

xy-y=3

dy/dx=-y/(x-1)

400

Differentiate this function implicitly.

x³y³-y=x

dy/dx=1/(3x²y²-1)

500

Differentiate this function implicitly.

x³+y³=xy

dy/dx=(y-3x²)/(3y²-x)

Random!

100

Find the derivative of this function.

f(x)=e^5x+3

f'(x)=5e^5x+3

200

Find the fourth derivative of this function.

f(x)=3x⁵+2x³-6x+4

f''''(x)=360x

300

Find the fifth derivative of this function.

f(x)=sin(x)

f⁽⁵⁾(x)=cos(x)

400

Using the limit definition of a derivative, find the derivative, f(x), of the limit below.

lim as h→0 of [3(1+h)²-7(1+h)+1+(3)]/h

f(x)=3x²-7x+1

500

Find the derivative of this function.

f(x)=tan^-1(x)

f'(x)=1/(1+x²)