Let for . Evaluate exactly and simplify your…

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

Problem

Let

f(x)=x\arccos x+\sqrt{1-x^{2}}

for

-1<x<1

. Evaluate

f'\!\left(\tfrac12\right)

exactly and simplify your answer.

Related theory

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

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