Let $u$ be a function such that $|u|^{(p-2)/2}u$ is in $H^1_0(G)$, $G$ is open and $p>2$.

How can I show that 

$$D(|u|^{(p-2)/2}u)=p/2|u|^{(p-2)/2}D(u) \quad(1)$$

(1) is stated in the proof of Lemma 1 in a work of Raviart "Sur la résolution et l'approximation de certaines équations paraboliques non linéaires dégénérées"
published about 1967.