If $f\left( x \right) = {\log _x}({\log _e}x),$ then $f'\left( x \right)$ at $x = e$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f\left( x \right) = {\log _x}({\log _e}x),

then

f'\left( x \right)

x = e

is equal to

View answer and explanation

Correct option: D

\frac{1}{e}

Option D (

\frac{1}{e}

) is correct because after differentiating the given function and substituting x = e, the result simplifies to

\frac{1}{e}

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