Question

If \[y = \log \left| 3x \right|, x \neq 0, \text{ find } \frac{dy}{dx} \] ? 

Answer 1

\[\text{ We have, y } = \log\left| 3x \right|\]

\[\Rightarrow \frac{dy}{dx} = \frac{d}{dx}\left( \log\left| 3x \right| \right)\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{3x}\frac{d}{dx}\left( 3x \right)\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{3x}\left( 3 \right)\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x}\]