Teaching UP PGT Mock Test Series 2024 Mathematics Differential Calculus Evaluation of derivatives

If \( f(x)=\cos^{-1}\left[\dfrac{1-(\log x)^2}{1+(\log x)^2}\right] \), then \( f'(e)= \) _________.

1
\( \dfrac{1}{e} \)
2
\( \dfrac{2}{e^2} \)
3
\( \dfrac{2}{e} \)
4
None of these
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