# Category:Differentiable Real Functions

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This category contains results about Differentiable Real Functions.

Definitions specific to this category can be found in Definitions/Differentiable Real Functions.

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

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

#### Definition 1

$f$ is **differentiable at the point $\xi$** if and only if the limit:

- $\displaystyle \lim_{x \mathop \to \xi} \frac {\map f x - \map f \xi} {x - \xi}$

exists.

#### Definition 2

$f$ is **differentiable at the point $\xi$** if and only if the limit:

- $\displaystyle \lim_{h \mathop \to 0} \frac {\map f {\xi + h} - \map f \xi} h$

exists.

These limits, if they exist, are called the derivative of $f$ at $\xi$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Differentiable Real Functions"

The following 8 pages are in this category, out of 8 total.