Changing variable in partial derivative's

Question

I have $u\colon:\mathbb{R}^n\times(0,\infty)\to\mathbb{R}$ smooth, $u=u(x,y)$. Consider the following changing of variables: $$ z=\biggl(\frac{y}{1-a}\biggr)^{1-a},$$ where $a\in(-1,1)$, i want to prove that: \begin{equation} y^au_y=u_z. \end{equation} I have found this change of variables in link. I tried to apply the chain rule but without success. Any help would be appreciated.