Calculus Derivatives

Basic Derivatives

100

y = 3x², find y'

y' = 6x

200

f(x) = 5, find f'(x)

0

300

f(x) = 6x³ + x - 2, find f'(x)

18x² + 1

400

f(x) = 3sinx - 2cosx, find f'(x)

3cosx + 2sinx

500

f(x) = 2e^x - 3ln(x), find f'(x)

2e^x - 3/x

Product and Quotient Rule

100

y = 3x² sin x, find y'

3x² cos x + 6x sin x

200

f(x) = (3x - 2x²)(5 + 4x), find f'(x)

-24x² + 4x + 15 or 4(3x - 2x²) + (3-4x)(5+4x)

300

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

(-5x² + 4x + 5)/(x² + 1)²

400

f(x) = (2x + 5)/(x)^1/2, find f'(x) and simplify

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

500

y = ln(x)/e^x, find y' and simplify

(1-xln(x))/xe^x

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) = e^sin(x), find f'(x)

cos(x)e^sin(x)

Abstract Thinking

100

f(x) = 3x² + 8sin(x), find f'(x) AND f''(x)

f'(x) = 6x + 8 cos(x)

f''(x) = 6 - 8 sin(x)

200

f(x) = sqrt(x), find the domain of f'(x)

x>0

300

Suppose f'(x) = x³-3x², find any function f(x) that would make this true

x⁴/4 - x³

400

f(x) = ln(213x⁷⁵), find f'(x)

75/x

500

Find the derivative of sin³⁵⁴(196³¹²⁸)/cos⁶(12/16⁵⁴⁸)

0

Random Trivia

100

What is the name of the dog in The Grinch?

Max

200

What is the capital city of Canada?

Ottawa

300

Who painted Starry Night?

Vincent Van Gogh

400

How many hearts does an octapus have?

3

500

What does HTTP stand for?

hypertext transfer protocol