If , then which of the following is (are)…

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

Problem

If f(x)=sin⁡−11+x2−121+x2f(x)=\sin^{-1}\sqrt{\frac{\sqrt{1+x^2}-1}{2\sqrt{1+x^2}}}, then which of the following is (are) correct? (a) f′(−1)=−14f'(-1)=\frac{-1}{4} (b) f′(1)=14f'(1)=\frac{1}{4} (c) f(x)f(x) is an odd function (d) f(x)f(x) is an even function

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