The function is differentiable for all real

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

Problem

The function

g(x)= \tan^{-1}(x)

is differentiable for all real

x

. Explain why

x=0

is not a critical point of

g

Related theory

Advanced Differentiation
Curve Analysis
Derivatives of standard functions via chain rule
Derivatives of inverse trigonometric functions
Continuity and Differentiability

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