Derivatives Review

Power Rule

100

f(x) = 6x³ - 9x + 4

f'(x) = 18x² - 9

200

f(x) = 4x⁷ - 3x^-7 + 9x

f'(x) = 28x⁶ + 3x^-8 + 9

300

y = 1 / x³

y' = -3 / x⁴

400

g(x) = x(3x² - 9)

g'(x) = 9x² - 9

500

f(x) = (x - 4)(2x + x²)

f'(x) = 3x² - 4x - 8

Products and Quotients

100

g(x) = x(2^x)

g'(x) = 2^x + x2^x(ln 2)

200

g(x) = xe^x

g'(x) = e^x + xe^x

300

f(x) = x² / sin(x)

f'(x) = [2xsin(x) - x²cos(x)] / sin²(x)

400

h(x) = (x²)(3^x)

h'(x) = 2x(3^x) + x²(3^x ln(3))

500

g(x) = sin(x) / e^x

g'(x) = [e^x cosx - e^x sin(x)] / e^2x

Trig Functions

100

g(x) = cos(x)

g'(x) = -sin(x)

200

f(x) = tan(x)

f'(x) = sec²(x)

300

f(x) = x sin(x)

f'(x) = sin(x) + x cos(x)

400

h(x) = tan(x) sec(x)

h'(x) = sec³(x) + sec(x)tan²(x)

500

f(x) = x² cos(x)

f(x) = 2x cos(x) - x² sin(x)

Chain Rule

100

f(x) = e^2x

f'(x) = 2e^2x

200

f(x) = cos(5x)

f'(x) = -5 sin(5x)

300

f(x) = cos(x⁵)

f'(x) = -sin(x⁵)(5x⁴)

400

g(x) = e^sin(x)

g'(x) = e^sin(x)(cos x)

500

h(x) = 2^sin(3x)

h'(x) = 2^sin(3x)(ln 2)(cos(3x))*3

Trivia!

100

In what city did Mr. Dooley teach last year?

Jacksonville, Florida

200

Name one of the teams in Super Bowl LVIII (2024).

Kansas City Chiefs and San Francisco 49ers

300

What is the capital of Canada?

Ottawa

400

How many moons orbit the planet Mars?

Two (Phobos and Deimos)

500

What year did the Civil War end? (guess within 5 years)

1865 (Acceptable: 1860 - 1870)