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 $a = \tuple {a_1, a_2, \ldots, a_n}^\intercal \in U$.

Let $f$ be differentiable at $a$.

Let $i \in \set {1, 2, \ldots, n}$.

Also see

 * Equivalence of Definitions of Partial Derivative of Real Valued Function at Point