I am trying to understand the chain rule under a change of variables. Given a function $f : \mathbb R^n \rightarrow \mathbb R$ and a change of variables $G : \mathbb R^m \rightarrow \mathbb R^n$, what is the derivative

$\partial^\alpha ( f \circ G )$

where $\alpha$ is a multiindex in the variables $x_1,\dots,x_m$ of degree $k$? We assume all necessary derivatives exist. References to the literature would be helpful too. I haven't found this general case treated in my sources.