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

e

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\frac{1}{e}

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1

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N o n e o f t h e s e

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Solution

The correct option is B $\frac{1}{e}$
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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If f(x)=logx(logx), then f′(x) at x=e is

The correct option is B 1eGiven f(x)=log(logx)Differentiate it with respect to xf′(x)=1logx.1xSubstituting x=ef′(x)=1loge.1ef′(x)=1e

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

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