Unit 3: Differentiation: composite, implicit, and inverse functions

Flashcards for Unit 3 of AP Calculus

Composite function

Chain Rule (general form)

Implicit function

x and y are mixed in the same equation

Key rule for implicit differentiation

d/dx(y^n) = n·y^(n−1)·dy/dx

Inverse function

Reverses the original function

Derivative of inverse function (key formula)

Derivative of inverse function at a point

Derivative of arcsin(x)

Derivative of arccos(x)

d/dx(cos⁻¹x) = −1 / √(1 − x²)

Derivative of arctan(x)

Derivative of sin(x)

cos(x)

Derivative of cos(x)

−sin(x)

Derivative of tan(x)

sec²(x)

Derivative of sec(x)

sec(x)tan(x)

Derivative of csc(x)

−csc(x)cot(x)

Derivative of cot(x)

−csc²(x)

Log rule: product

Log rule: power

Derivative of ln(x)

d/dx(ln x) = 1/x