Definition:Differentiable Mapping/Real Function/Point/Definition 2

Definition
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 $\xi$ the limit:
 * $\ds \lim_{h \mathop \to 0} \frac {\map f {\xi + h} - \map f \xi} h$

exists.