Let $U \subset \mathbb{R}^m$ and $V \subset \mathbb{R}^n$ be open sets, let $a \in U$, let $g: U \to V$ be twice differentiable at $a$, and let $f: V \to \mathbb{R}^p$ be twice differentiable at $g(a)$. Then the composition $f \circ g: U \to \mathbb{R}^p$ is twice differentiable at $a$, and for every $h,k \in \mathbb{R}^m$,