Definition:Differentiable Mapping/Real-Valued Function/Point

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

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

Let $x \in U$.

Also see

 * Equivalence of Definitions of Differentiable Real-Valued Function at Point
 * Definition:Partial Derivative of Real-Valued Function
 * Characterization of Differentiability for clarification of this definition.