\begin{definition}[Definition:Differential of Mapping/Real Function/Point]
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 $x$.
Category:Definitions/Differentials
\end{definition}