#### Answer

$f'(0)$ is undefined.

#### Work Step by Step

Using the rule that $\dfrac{d}{dx}|z(x)|=z'(x)\dfrac{|z(x)|}{z(x)}\to$
$f'(x)=0-(1\times\dfrac{|x|}{x})=-\dfrac{|x|}{x}; x\ne0.$
$f'(0)$ is undefined because the left-side limit of +1 does not agree with the right-hand limit of -1. This can also be seen from the graph.