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Question
If \[y = \log \left| 3x \right|, x \neq 0, \text{ find } \frac{dy}{dx} \] ?
Solution
\[\text{ We have, y } = \log\left| 3x \right|\]
\[\Rightarrow \frac{dy}{dx} = \frac{d}{dx}\left( \log\left| 3x \right| \right)\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{3x}\frac{d}{dx}\left( 3x \right)\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{3x}\left( 3 \right)\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x}\]
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