Solution
= Solution
If $F:U\subseteq\mathbb R^n\to\mathbb R^m$ is differentiable at $x$, and $G$ is defined on a neighborhood of $F(x)$ and differentiable there, the <chain rule> states
$$
\boxed{D(G\circ F)_x=DG_{F(x)}\circ DF_x.}
$$
In standard coordinates the same statement is
$$
\boxed{J_{G\circ F}(x)=J_G(F(x))J_F(x).}
$$
The evaluation point in the first factor is $F(x)$, and the <matrix> order follows the order in which the <linear maps> act on increments.