A differentiable function satisfies for every in its domain

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

A differentiable function

f

satisfies

f'(x)\neq 0

for every

x

in its domain. In one or two sentences, explain why this condition ensures that the inverse function

f^{-1}

is also differentiable wherever it exists.

Related theory

Derivatives of Inverse Functions
Advanced Differentiation

Browse the problem library