If $f(x)=\log |x|, x \neq 0$ then f'(x) equals

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

$\frac{1}{x}$

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