Explanation: $\mathit{f}\left(\mathit{x}\right)=\mathit{x}|\mathit{x}|,\mathit{x}\in \mathrm{R}$ is differentiable. if $\mathit{x}\ne 0$,
then the function is quadratic so is differentiable.
The only point to consider is 0 . But since both ${\mathit{x}}^2$ and $-{\mathit{x}}^2$ have same derivative at 0 , then it follows that $\mathit{f}$ is differentiable at 0 .