Identify the general relationship between and for a function that is differentiable…

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

Problem

Identify the general relationship between

(f^{-1})'(x)

and

f'(f^{-1}(x))

for a function

f

that is differentiable and has a differentiable inverse.

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Functions
Functions and invertibility
Relations and Functions
Invertible functions and inverse of a function

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