Definition:Differentiable Mapping/Real-Valued Function/Open Set
Jump to navigation
Jump to search
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