Choose the correct alternative in the following:

Question:

Choose the correct alternative in the following:

The differential coefficient of $f(\log x)$ with respect to $x$, where $f(x)=\log x$ is

A. $\frac{\mathrm{x}}{\log \mathrm{x}}$

B. $\frac{\log x}{x}$

C. $(x \log x)^{-1}$

D. none of these

Solution:

Given: $f(x)=\log x$

$\therefore f(\log x)=\log (\log x)$

$f^{\prime}(\log x)=\frac{d}{d x} \log (\log x)$

$f^{\prime}(\log x)=\frac{1}{\log x} \cdot \frac{1}{x}=\frac{1}{x \log x}$

$\therefore f^{\prime}(\log x)=(x \log x)^{-1}$

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