Let $n,m \in \mathbb N$, let $U \subset \mathbb R^n$ be open, let $f \in C^1(U;\mathbb R^m)$, and let $K \subset U$ be nonempty, compact, and convex. Then, for every $x,y \in K$,
Here $Df_z:\mathbb R^n \to \mathbb R^m$ denotes the total derivative of $f$ at $z$, and $\|\cdot\|_{\mathrm{op}}$ is the operator norm induced by the Euclidean norms on $\mathbb R^n$ and $\mathbb R^m$.