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

500

y=tanx

y=sec²x

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)

500

y=x³(5x-1)⁴

3x²(5x-1)⁴+20x³(5x-1)³

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

500

y=(2x+3)^(1/2)

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

Find the slope

100

Find the slope y=x² + 30 at x=1

slope = 2

200

y=sin x + cos x x=(pi/2)

slope = -1

300

y=tanx x=0

slope=1

400

y= x³ - 3x² + 2x - 12 x=3

x=11

500

y=(3x-8)⁴ x=2

slope = -96