Calculus Derivatives

Basic Derivatives

100

Find the derivative of f(x) = 5

0

200

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

18x² + 1

300

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

3cosx + 2sinx

Product and Quotient Rule

100

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

200

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

(-5x² + 4x + 5)/(x² + 1)²

300

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

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

Chain Rule

100

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

4 cos 4x

200

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

300

f(x) = sin³ 4x Find f'(x)

12sin² 4x cos 4x

Implicit Differentiation

100

sin x + 2cos 2y = 1

y' = cosx/4sin2y

200

(y - 2)² = 4x - 12

y' = 2/(y - 2)

300

x³ - 3x²y + 2xy² = 12

y' = (-3x² + 6xy - 2y²)/(-3x² + 4xy)