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.

When $x<0$ replace $|x|$ by $-x$ (since that is what it is equal to) in the formula for the function and proceed. 
Please note as well that the function $f(x)=x\cdot |x|$ does have a derivative at $0$.
