Derivatives

Basic Derivatives

100

What is the derivative of y = 3x² ?

y' = 6x

200

Find the derivative of f(x) = e^π 

0

300

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

18x² + 1

400

Find the derivative of 1/x

-1/x²

500

Find the derivative of ln(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 (2x+5)(x+9)/(x+3)

(x+3)(2(x+9)+2x+5)−(x+9)(2x+5)/(x+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

500

f(x) = cos(4e^x) Find f'(x)

−4e^xsin(4e^x) 

Trigonometric Functions

100

tan(x) + cot(x)

sec²(x)-csc²(x)

200

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

3cosx + 2sinx

300

Find the derivative of f(x) =2sec(x)+4csc(x)

2sec(x)tan(x)−4cot(x)csc(x)

400

Find the derivative of sin(cos(x))

−sin(x)cos(cos(x))

500

csc(2x)sec(x)

sec(x)tan(x)csc(2x)−2sec(x)cot(2x)csc(2x)