If \( f(x)=\cos ^{-1}\left\{\frac{1-\left(\log _{e} x\right)^{2}}{1...

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If \( f(x)=\cos ^{-1}\left\{\frac{1-\left(\log _{e} x\right)^{2}}{1+\left(\log _{e} x\right)^{2}}\right\} \), then \( f^{\prime}(e) \)
\( \mathrm{P} \)
W
(A) Does not exist
(B) Is equal to \( \frac{2}{e} \)
(C) Is equal to \( \frac{1}{e} \)
(D) Is equal to 1
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