Chain rule

Let $U\subseteq\mathbb R^k$ and $V\subseteq\mathbb R^m$ be open sets. If $f:U\to V$ is differentiable at $a\in U$ and $g:V\to\mathbb R^p$ is differentiable at $f(a)$, then the composition $g\circ f$ is differentiable at $a$, and

In terms of Jacobian matrices, this is