Describe the set of all real numbers for which the derivative of exists

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

Problem

Describe the set of all real numbers

x

for which the derivative of

f(x)=\arcsin(\arctan x)

exists, and briefly justify your answer.

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of inverse trigonometric functions
Continuity and Differentiability

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