Prove that if $f |f|$ differentiable in $a$ and $f(a)= 0$, then $f$ is differentiable in $a$.
The only thing i know is that $|f´|(a) = 0$
I don´t know how to start with the demostration, i´ve tried appling the definition of derivative but don´t know how to continue.
There's an example that does not work.
If $f(x)=|x|$, then $f(x)|f(x)| = x^2$ which is differentiable on $x=0$, and $f(0)=0$.
But, $f(x)$ is not differentiable on $x=0$.