Answer
$f'(x) = \frac{g'(x)}{g(x)}$
Work Step by Step
Let $h(x) = ln~\vert x \vert$
$h'(x) = \frac{1}{x}$
We can find $f'$:
$f(x) = ln~\vert g(x) \vert$
$f(x) = h(g(x))$
$f'(x) = h'(g(x))~\cdot g'(x)$
$f'(x) = \frac{1}{g(x)}\cdot g'(x)$
$f'(x) = \frac{g'(x)}{g(x)}$
