Briefly explain why the derivative is undefined if for some value .

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

Problem

Briefly explain why the derivative

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

is undefined if

f'(f^{-1}(a))=0

for some value

a

Related theory

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

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