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