Let $n\in\mathbb{N}$, let $U\subseteq \mathbb{R}^n$ be \reftext{def:open-subset-euclidean-space-2026a}{open}, let $f:U\to\mathbb{R}$ be a \reftext{def:c1-map-euclidean-open-set-2026a}{$C^1$ map}, let $i\in\{1,\dots,n\}$, and let $x=(x_1,\dots,x_n)\in U$. Let $a,b\in\mathbb{R}$ with $a<b$, and assume that

Define $g:[a,b]\to\mathbb{R}$ by

Then $g$ is continuous on $[a,b]$, differentiable at every $t\in(a,b)$, and

for every $t\in(a,b)$.