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

How can I show that 

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

or how can I show that 

$$u\in W^{1,p}_0(G) \quad (2).$$

Note that (2) implies (1).