\begin{definition}[Definition:Differentiable Mapping/Real Function/Point/Definition 1]
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:
:$\ds \lim_{x \mathop \to \xi} \frac {\map f x - \map f \xi} {x - \xi}$
exists.
\end{definition}