Equality p-Laplacian

Question

Prove that $$\Delta_p u= \text{div}(|\nabla u|^{p-2}\nabla u)=|\nabla u|^{p-2} ({(p-2)\Delta_{\infty}} u+\Delta u)$$

I tried do this from the definitions but it didn't lead me to the any good conclusion.

Thanks in advance.