Definition:Differentiable Mapping/Real Function/Point/Definition 1

Definition
Let $f$ be a real function defined on an open interval $\openint a b$.

Let $\xi$ be a point in $\openint a b$.

Then $f$ is differentiable at the point $\xi$ the limit:
 * $\displaystyle \lim_{x \mathop \to \xi} \frac {\map f x - \map f \xi} {x - \xi}$

exists.