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JEE MATHEMATICS MCQ: DIFFERENTIATION

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If f(x)=tan⁡−1(2x1−x2),x∈Rf(x)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right), x \in R, then f′(x)f^{\prime}(x) is given by
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Correct option: A
f′(x)=21+x2f^{\prime}(x)=\frac{2}{1+x^2} for all x∈R−{−1,1}x \in R-\{-1,1\}
Option A is correct because the derivative of arctan(2x/(1-x2)) is 2/(1+x2) for all x in R - {-1,1}, where the function is not continuous.

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