If $y = {\cos ^{ - 1}}\left( {\frac{{1 - \log x}}{{1 + \log x}}} \right),$ then $\frac{{dy}}{{dx}}$ at $x = e$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y = {\cos ^{ - 1}}\left( {\frac{{1 - \log x}}{{1 + \log x}}} \right),

then

\frac{{dy}}{{dx}}

x = e

View answer and explanation

Correct option: C

\frac{1}{{2e}}

Option C (

\frac{1}{{2e}}

) is correct because after differentiating and substituting

x = e

, the derivative evaluates to

\frac{1}{{2e}}

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