If $f(x)=\log |2 x|, x \neq 0$ then f'(x) is equal to

$\frac{1}{x}$ $-\frac{1}{x}$ $\frac{1}{|x|}$ none of these

$\frac{1}{x}$

We have, $f(x)=\log |2 x| \begin{cases}\log 2 x, & x>0 \\ \log (-2 x), & x<0\end{cases}$ $\Rightarrow f'(x)=\left\{\begin{aligned} \frac{1}{2 x} \times 2 & =\frac{1}{x}, & & x>0 \\ -\frac{1}{2 x} \times-2 & =\frac{1}{x}, & & x<0\end{aligned}\right.$ $\Rightarrow f'(x)=\frac{1}{x}$  for all  $x \neq 0$.