Explain, in no more than two sentences, why the denominator appears in the derivative…

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

Problem

Explain, in no more than two sentences, why the denominator

\sqrt{1-x^{2}}

appears in the derivative of

\arcsin x

for

|x|<1

Related theory

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

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