How do I calculate the derivative of $x|x|$? I know that $$f(x)=x\cdot|x|$$ have no derivative at $$x=0$$ but how do I calculate it's derivative for the rest of the points?
When I  calculate for $$x>0$$ I get that $$f'(x) = 2x $$
but for $$ x < 0 $$ I can't seem to find a way to solve the limit. As this is homework please don't put the answer straight forward.

Hint If $x\gt 0$ we are looking at $x^2$, easy. If $x\lt 0$, we are looking at $-x^2$, easy. For $x=0$, use the definition of the derivative.
So at $0$ we want $\displaystyle\lim_{h\to 0}\,\dots$,
