Question

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

Options

• \[\frac{x}{\log x}\]

• \[\frac{\log x}{x}\]

• \[\left( x \log x \right)^{- 1}\]

• none of these

Answer 1

\[\left( x \log x \right)^{- 1}\] 

We have,

\[f\left( x \right) = \log x\]
\[ \Rightarrow f\left( \log x \right) = \log\left( \log x \right)\]
\[ \Rightarrow f'\left( \log x \right) = \frac{1}{\log x}\frac{d}{dx}\left( \log x \right)\]
\[ \Rightarrow f'\left( \log x \right) = \frac{1}{x \log x}\]
\[ \Rightarrow f'\left( \log x \right) = \left( x \log x \right)^{- 1}\]