If $f(x)=\log _{x^{\prime}}(\log x)$, then $f^{\prime}(x)$ at $x=e$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f(x)=\log _{x^{\prime}}(\log x)

, then

f^{\prime}(x)

x=e

View answer and explanation

Correct option: D

\frac{1}{2 e}

Option D (

\frac{1}{2 e}

) is correct because after simplifying the function and finding its derivative, the value of

f'(e)

\frac{1}{2e}

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