Let $U \subset \mathbb{R}^m$ be open, let $a \in U$, let $u,v \in \mathbb{R}^m$, and let $f,g: U \to \mathbb{R}^n$ be functions. Suppose that there exists an open neighbourhood $W \subset U$ of $a$ such that
paragraph
admin
\begin{align*}
f(x)=g(x) \quad \text{for every } x \in W.
\end{align*}
latex_env
admin
For a function $h:U\to\mathbb{R}^n$, write $D_vh(x)$ for the limit