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)

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

500

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

(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) = sin(4x)³ Find f'(x)

12sin(4x)² 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(t) = 1/t, find f'(t)

f'(t) = -t^-2 = -1/t²

300

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

x⁴/4 - x³

400

f(x) = ln(x⁷⁵), find f'(x)

75/x

500

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

0

Random Trivia

100

What company owns ChatGPT?

OpenAI

200

Name all official languages of Aotearoa.

Te Reo Māori, NZ Sign Language, and English

300

Who built Machu Picchu?

Inca Empire

400

How many hearts does an octapus have?

3

500

Name any three stars of Matariki?

Pōhutukawa, Tipuānuku, Tipuārangi, Waitī, Waitā, Waipunarangi, Ururangi, Hiwa-i-te-Rangi, and Matariki