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 y=1/2x³+4x²-1/3x

y'=3/2x²+8x-1/3

500

The derivative of 13x⁴ + 3x² - 6x +3

What is 52x³ + 6x - 6

Product and Quotient Rule

100

Find the derivative of y = 3x² (7x+2)

y'=3x²(7)+(7x+2)(6x)

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 3x(5x³-2x)

What is 3x(15x²-2)+(5x³-2x)(3)

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

Find the derivative of f(x) = (4x⁴+5x)⁹

y'=9(4x⁴+5x)⁸(16x³+5)

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

400

f(x) = -2(6x²+3x)³. Find f'(x)

-6(6x²+3x)²(12x+3)

500

The derivative of y=6(9x²+4)⁷

y'=42(9x²+4)⁶(18x)

Logarithmic and Exponential Derivatives

100

Find the derivative of y = e^x. 

y' = e^x

200

f(x) = ln(x²)

2/x

300

f(x) = 3^x2

f'(x) = 2x ln3 3^x2

400

f(x) = ln(4x⁴-9x)

f'(x) =[ 1/(4x⁴-9x)]*(16x³-9)

500

y = log₄(8x²+3x-5)

y'=[1/ln(4)(8x²+3x-5)]*(16x+3)