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

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Q. The differential coefficient of $f \left(\log _{ e } x \right)$ w.r.t. $x$ where $f ( x )=\log _{ e } x$ is

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Solution:

$f \left(\log _{ e } x \right)=\log _{ e }\left(\log _{ e } x \right) \quad \frac{d}{d x}(\log (\log x))=\frac{1}{\log x} \cdot \frac{1}{x}$