Assertion: Statement I Derivative of w.r.t

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

Problem

Assertion: Statement I Derivative of sin⁡−1(2x1+x2)\sin^{-1}\left(\frac{2x}{1+x^2}\right) w.r.t.cos⁡−1(1−x21+x2)\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) is 1 for 0<x<10 < x < 1 . Reason: Statement II sin⁡−1(2x1+x2)=cos⁡−1(1−x21+x2)\sin^{-1}\left(\frac{2x}{1+x^2}\right) = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) for −1≤x≤1-1 \le x \le 1

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