Question

State true or false:

The differential coefficient of $f\left(\log x\right)$ w.r.t. $\log x$ where $f\left(x\right)=\log x$ is $\frac{1}{\log x}$.

• A. True
• B. False

Answer 1

The correct option is A True

$f\left(\log x\right)=\log \left(\log x\right)$
$\therefore \frac{d}{dx}\left(f\left(\log x\right)\right)=\frac{1}{\log x}\frac{1}{x}$
And $\frac{d\left(\log x\right)}{dx}=\frac{1}{x}$
Therefore derivative of $f\left(\log x\right)$ w.r.t $\log x$ is
$\frac{\frac{1}{x\log x}}{\frac{1}{x}}=\frac{1}{\log x}$