[viista]

Let $f$ be differentiable on $(a,b)$. Put
$$
f^+(x)=\left\{\begin{array}{c}
f(x)&\text{for }f(x)>0\\
0&\text{for }f(x)\leq0.
\end{array}\right.
$$
Show that $(f^+)^2$ is differentiable on $(a,b)$, and that its derivative is given by $2f^+(x)f'(x)$ at each $x$ in $(a,b)$.