Calculus Derivatives

Basic Derivatives

100

What is the derivative of y = 3x² ?

y' = 6x

200

Find the derivative of f(x) = 5

0

300

Find the derivative of f(x) = 6x³ + x - 2

18x² + 1

400

Find the derivative of f(x) = 3sinx - 2cosx

3cosx + 2sinx

Product and Quotient Rule

100

Find the derivative of y = 3x² sin x

3x² cos x + 6x sin x

200

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

300

Find the derivative of y = (5x - 2)/(x² + 1)

(-5x² + 4x + 5)/(x² + 1)²

400

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

Find the derivative of f(x) = sin 4x

4 cos 4x

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

400

f(x) = sin³ 4x Find f'(x)

12sin² 4x cos 4x

Function Operations

100

Find ( g x h)(1) when g(n)=n^2+4+2n and h(n)=-3n+2

-7

200

Find (f-g)(4) when f(x)=4x-3 and g(x)=x^3+2x

-59

300

Find (f/g)(x) when f(x)=3x-1 and g(x)=x^2-x.

(3x-1)/(x^2-x)

400

Find g(f(2)) when g(n)=3n+2 and f(n)=2n^2+5

41

500

Find g(f(x)(-2+x) when g(x)-2x-2 and f(x)=x^2+3x

2x^2-2x-6