Let $U \subset \mathbb R^n$ be open. The partial derivative of a function $f:U\to\mathbb R^m$ with respect to the $i$th coordinate $x_i$ at $a = (a_1,\dots,a_n) \in U$ is defined as \(\frac{\partial f}{\partial x_i}(a) = \lim_{h\to 0} \frac{f(a_1,\dots,a_i+h,\dots,a_n) - f(a)}{h}.\)
Wikidata ID: Q186475