Definition:Differentiable Mapping/Real-Valued Function/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 $\mathbb X$.


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