Definition:Differential of Mapping/Real Function/Point
< Definition:Differential of Mapping | Real Function(Redirected from Definition:Differential of Real Function at Point)
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Definition
Let $U \subset \R$ be an open set.
Let $f: U \to \R$ be a real function.
Let $f$ be differentiable at a point $x \in U$.
The differential of $f$ at $x$ is the linear transformation $\map {\d f} x : \R \to \R$ defined as:
- $\map {\map {\d f} x} h = \map {f'} x \cdot h$
where $\map {f'} x$ is the derivative of $f$ at $x$.