# Definition:Differentiable Mapping/Real-Valued Function/Open Set

< Definition:Differentiable Mapping | Real-Valued Function(Redirected from Definition:Differentiable Real-Valued Function on Open Set)

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## Definition

Let $\mathbb X$ be an open subset of $\R^n$.

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

Then $f$ is **differentiable in the open set $\mathbb X$** if and only if $f$ is differentiable at each point of $\mathbb X$.

## Also see

- Characterization of Differentiability for clarification of this definition.
- Definition:Continuously Differentiable Vector-Valued Function