\begin{definition}[Definition:Partial Derivative/Real Analysis/Point]
Let $U \subset \R^n$ be an open set.
Let $f: U \to \R$ be a real-valued function.
Let $a = \tuple {a_1, a_2, \ldots, a_n}^\intercal \in U$.
Let $f$ be differentiable at $a$.
Let $i \in \set {1, 2, \ldots, n}$.
\end{definition}