\begin{definition}[Definition:Derivative/Higher Derivatives/Second Derivative]
Let $f$ be a real function which is differentiable on an open interval $I$.
Hence $f'$ is defined on $I$ as the derivative of $f$.
Let $\xi \in I$ be a point in $I$.
Let $f'$ be differentiable at the point $\xi$.
Then the '''second derivative''' $\map {f''} \xi$ is defined as:
:$\ds f'' := \lim_{x \mathop \to \xi} \dfrac {\map {f'} x - \map {f'} \xi} {x - \xi}$
Thus the '''second derivative''' is defined as the derivative of the first derivative.
If $f'$ is differentiable, then it is said that $f$ is '''doubly differentiable''', or '''twice differentiable'''.
\end{definition}