# Category:Second Derivatives

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This category contains results about **Second Derivatives**.

Definitions specific to this category can be found in **Definitions/Second Derivatives**.

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:

- $\ds f' ' := \lim_{x \mathop \to \xi} \dfrac {\map {f'} x - \map {f'} \xi} {x - \xi}$

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