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Question

If $f (x) = {log}_{x} (log x)$ , then $f^{'} (x)$ at $x = e$ is
$e$
$\frac{1}{e}$
$1$
$N o n e o f t h e s e$

A

e

B

\frac{1}{e}

C

1

D

N o n e o f t h e s e

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Solution

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Given
$f (x) = log (log x)$
Differentiate it with respect to $x$
$f^{'} (x) = \frac{1}{log x} . \frac{1}{x}$
Substituting $x = e$
$f^{'} (x) = \frac{1}{log e} . \frac{1}{e}$
$f^{'} (x) = \frac{1}{e}$

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