\begin{definition}[Definition:Derivative/Real Function/Derivative at Point/Definition 1]
Let $I$ be an open real interval.
Let $f: I \to \R$ be a real function defined on $I$.
Let $\xi \in I$ be a point in $I$.
Let $f$ be differentiable at the point $\xi$.
That is, suppose the limit $\ds \lim_{x \mathop \to \xi} \frac {\map f x - \map f \xi} {x - \xi}$ exists.
Then this limit is called the '''derivative of $f$ at the point $\xi$'''.
\end{definition}