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JEE MATHEMATICS MCQ: DIFFERENTIATION

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If f(x)=sin⁡−1(2x1−x2),x∈[−1,1]f(x)=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right), x \in[-1,1] Then,
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Correct option: B
f′(x)={21−x2, if ∣x∣<12−21−x2, if 12<∣x∣<1f^{\prime}(x)=\left\{\begin{array}{l}\frac{2}{\sqrt{1-x^2}}, \text { if }|x|<\frac{1}{\sqrt{2}} \\ \frac{-2}{\sqrt{1-x^2}}, \text { if } \frac{1}{\sqrt{2}}<|x|<1\end{array}\right.
Option B is correct because the derivative of arcsin(2x*sqrt(1-x2)) is piecewise, being 2/sqrt(1-x2) for |x|<1/sqrt(2) and -2/sqrt(1-x2) for 1/sqrt(2)<|x|<1 due to the properties of arcsin.

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