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

Find the derivative of f(x) = e^x + ln x

f'(x) = e^x + 1/x

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

Find the derivative of f(x) = sin(2x³+1) / (4x⁴ + 6x³ + x²)

Extra $100 for answering in simplest factored form.

3x cos(2x³ + 1)  /  (8x +1)(x + 1)

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

Implicit Differentiation

100

Find the derivative implicitly x² + y² = 30

y' = - x/y

200

sin x + 2cos 2y = 1

y' = cosx/4sin2y

300

(y - 2)² = 4x - 12

y' = 2/(y - 2)

400

x³ - 3x²y + 2xy² = 12

y' = (-3x² + 6xy - 2y²)/(-3x² + 4xy)