Question

If $y=\log \left|3x\right|,x\ne 0,\mathrm{find}\frac{dy}{dx}.$

Answer 1

$\mathrm{We}\mathrm{have},y=\log \left|3x\right|$
$$\begin{gathered} \Rightarrow \frac{dy}{dx}=\frac{d}{dx}\left(\log \left|3x\right|\right) \\ \Rightarrow \frac{dy}{dx}=\frac{1}{3x}\frac{d}{dx}\left(3x\right) \\ \Rightarrow \frac{dy}{dx}=\frac{1}{3x}\left(3\right) \\ \Rightarrow \frac{dy}{dx}=\frac{1}{x} \end{gathered}$$