AP Calculus Unit 2 Review

Differentiation Rules

100

Find the derivative of this function.

f(x)=3x^2+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-x^2)(5+4x)

f'(x)=-12x^2+10x+15

400

Find the derivative of this function.

f(x)=(7x + 4) / (x² + 5)

f'(x)= (-7x² - 8x + 35) / (x² + 5)² 

Differentiation with Trig

100

Find the derivative of this function

f(x)= 3sinx-4cosx

f'(x)=3cosx+4sinx

200

Find the derivative of this function.

f(x)=cos(2x)

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

300

Find the derivative of this function.

f(x)=(x^3)sin(5x)

f'(x)=(3x^2)sin(5x)+(5x^3)cos(5x)

400

Find the derivative of this function.

f(x)=-3sin(4x^2+5)

f'(x)=-24xcos(4x^2+5)

Instantaneous Rates of Change

100

The average rate of change of the function f given by f(x)=x^3+2x-5 on the closed interval [0, 4]

18

200

Find the slope of f(x)=(5/3)x^(3)-3x^(2)-1/x^(2) at x=-1

9

300

Find the line tangent to f(x) that goes through the point at x=-1 if f(x)= x^3+4x-1 in slope intercept form

y=7x-3

400

The definition of the derivative of the function is...

f'(x)= lim(h->0)  (f(x-h)-f(x))/h

Random

100

Find the fourth derivative of this function.

f(x)=3x^5+2x^3-6x+4

f''''(x)=360x

200

What year did Ms. H graduate SMHS?

2021

300

Find the derivative of this function.

f(x)=3e^(4x)

f'(x)=12e^(4x)