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) = 3sin(x) - 2cos(x)

3cos(x) + 2sin(x)

500

The derivative of 13x⁴ + 3x²  - 6x +3

What is 52x³ + 6x - 6?

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

The derivative of 3xsin(3x)

What is 3sin(3x) + 9xcos(3x)?

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

The derivative of sin²(3x)

What is 6sin(3x)cos(3x)

Trigonometric Derivatives

100

f(x) = sec x

f'(x) = sec x tan x

200

y = 3csc(2x)

y' = -6csc(2x)cot(2x)

300

f(x) = sin x tan x

f'(x) = cos x tan x + sin x sec²x

400

y = tan(sec x)

y' = sec x tan x sec²(sec x)

500

The derivative of sin(x)cos(x)/tan(x).

What is -2cos(x)sin(x)?

Logarithmic and Exponential Derivatives

100

Find the second derivative of y = e^x

y'' = e^x

200

f(x) = ln(x²)

2/x

300

f(x) = 3^x2 

f'(x) = 2x ln(3) 3^x2

400

f(x) = ln(x/(x² + 1))

f'(x) = (1/x) - (2x/(x² + 1))

500

y = 10log₄(6)/t

-10log₄(6)/t²