Chain rule in $\mathbb{R}^d$, with $d\ge 2$.

Question

Given $\Omega\subset\mathbb{R}^d$ be an open bounded set with Lipschitz boundary, let $v\in (H^1(\Omega))^d$, $\psi\in H^1(\Omega)$ $T_K(x):=B_K x+b_K$, where $B_K$ is a non-singular invertible matrix.

What I need to compute is

• $\nabla (\psi\circ T_K)$
• $D^\alpha(v\circ T_K)$, where $|\alpha|=m$ ($\alpha$ is a multiindex)

Could you give me some help? At least some hints.

Thank you very much!