Let be a differentiable function with an inverse near the point where

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

Problem

Let

f

be a differentiable function with an inverse near the point

(b,a)

where

f(b)=a

. State the formula that gives

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

in terms of

f'(b)

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability
Implicit and Parametric Differentiation

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