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  4. The differential coefficient of f( log x) w.r.t x, where f(x)= log x is:

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Q. The differential coefficient of $ f(\log x) $ w.r.t $ x, $ where $ f(x)=\log x $ is:

Bihar CECEBihar CECE 2004

Solution:

We have, $f(x)=\log x$
$\Rightarrow f(\log x)=\log \log x$
On differentiating w.r.t. $x$ on both sides, we get
$f'(\log x) \frac{1}{x}=\frac{1}{\log x} \cdot \frac{1}{x}$
$\Rightarrow f(\log x)=\frac{1}{\log x}$