\begin{definition}[Definition:Differentiable Mapping/Real Function/Point/Definition 2]
Let $f$ be a real function defined on an open interval $\openint a b$.
Let $\xi$ be a point in $\openint a b$.
$f$ is '''differentiable at the point $\xi$''' {{iff}} the limit:
:$\ds \lim_{h \mathop \to 0} \frac {\map f {\xi + h} - \map f \xi} h$
exists.
Category:Definitions/Differentiable Real Functions
\end{definition}