Let $U \subset \mathbb R^n$ be open and let $f:U\to\mathbb R^n$ be differentiable. Then its total derivative $Df(a)$ at a point $a\in U$ is given by the $m\times n$ matrix \(\left[ \frac{\partial f_j}{\partial x_i}(a)\right]_{i=1,j=1}^{n,m}\) where $f = (f_1,\dots, f_m)$ are the component functions of $f$. This matrix is called the Jacobian matrix of $f$ at $a$.
Wikidata ID: Q506041