Question

The differential coefficient of $f(\log x)$ when $f\left(x\right)=\log x$ is:

• A. $x\log x$
• B. $\frac{x}{\log x}$
• C. $\frac{1}{x\log x}$
• D. $\frac{\log x}{x}$

Answer 1

The correct option is C

$\frac{1}{x\log x}$

Differentiating to find the coefficient:

Given that: $f\left(x\right)=\log x$

Now,

$$\begin{gathered} f(\log x)=\log \left(\log x\right) \\ \Rightarrow f\text{'}(\log x)=\frac{1}{\log x}\times \frac{1}{x}\left[\because \frac{d}{dx}\log x=\frac{1}{x}\right] \\ \Rightarrow f\text{'}(\log x)=\frac{1}{x\log x} \end{gathered}$$

Hence, the correct answer is Option (C).