Definition:Partial Derivative/Real Analysis/Point

Definition
Let $U\subset\R^n$ be an open set.

Let $f : U \to \R$ be a real-valued function.

Let $a = (a_1,\ldots,a_n)^\intercal \in U$.

Let $f$ be differentiable at $a$.

Let $i\in\{1,\ldots, n\}$.