Answer
Does not exist.
Work Step by Step
$f(x)=\sqrt{|x|}$
$f'(c)=\lim\limits_{x \to c}\frac{f(x)-f(c)}{x-c}$
$f'(0)=\lim\limits_{x \to 0}\frac{\sqrt{|x|}-\sqrt{|0|}}{x-0}$
$f'(0)=\lim\limits_{x \to 0}\frac{\sqrt{|x|}}{x}$
$f'(0)=\frac{\sqrt{|0|}}{0}$
$f'(0)=\frac{0}{0}$
Does not exist.
