Unit 2 - AP Calculus Differentiation Rules MUIDS Q1 2023

Addition Rule (f + g)

f’ + g’

Subtraction Rule (f - g)

f’ - g’

Multiplication Rule (fg)

f’g + fg’

Division Rule (f / g)

(f’g - fg’) / (g²)

Power Rule (f(x) = x^n)

nx^(n-1)

Constant Rule (f(x) = c)

f’ = 0

Constant Multiple Rule (f(x) = cx)

f’ = c

Derivative of sin(x)

cos x

Derivative of cos(x)

-sin x

Derivative of tan(x)

sec²x

Derivative of cot(x)

-csc²x

Derivative of sec(x)

(tan x)(sec x)

Derivative of csc(x)

-(cot x)(csc x)

Exponential Rule (f(x) = a^x)

(a^x)(ln a)

Derivative of e^x (f(x) = e^x)

e^x

Logarithm Rule (f(x) = log_a(x))

1 / (x)(ln a)

Natural Logarithm Rule (f(x) = ln x)

1/x

Chain Rule (f(g(x)))

f’(g(x))*g’(x)

sin^-1(x)

1 / sqrt(1 - x²)

sec^-1(x)

1 / |x|*sqrt(x² - 1)

tan^-1(x)

1 / (x² + 1)

cos^-1(x)

-1 / sqrt(1 - x²)

csc^-1(x)

-1 / |x|*sqrt(x² - 1)

cot^-1(x)

-1 / (x² + 1)

Function Inverse Derivative (f^-1(x))

1 / f’(f^-1(x))