Let $n,m,p\in \mathbb{N}$. Let $U\subseteq \mathbb{R}^n$, $V\subseteq \mathbb{R}^m$, and $W\subseteq \mathbb{R}^p$ be \reftext{def:open-subset-euclidean-space-2026a}{open} subsets. Let $f:U\to V$ and $g:V\to W$ be \reftext{def:c1-map-euclidean-open-set-2026a}{$C^1$ maps}. Then the composition $g\circ f:U\to W$ is again of class $C^1$. Moreover, for every $a\in U$, the Jacobian matrices from \reftext{def:differentiable-map-at-point-euclidean-2026a}{the differentiability definition} satisfy

where the product on the right-hand side is the matrix product from \reftext{def:product-real-matrices-2026a}{the definition of matrix multiplication}.