If f(x)=log |x|, x ≠ 0 then f'(x) equals

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  $x \neq 0$.