If $f (x) = l o g_{e} (x)$ then the differential coefficient of $f (l o g_{e} x)$ with respect to x is

\frac{x}{{log}_{e} x}

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\frac{{log}_{e} x}{x}

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\frac{1}{x {log}_{e} x}

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None of these

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Solution

The correct option is C $\frac{1}{x {log}_{e} x}$
$f = l n x$
$f (l n x) = l n l n x$
$f^{'} (l n x) = \frac{1}{x l n x}$

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