# Category:Differentiability Classes

Jump to navigation
Jump to search

This category contains results about Differentiability Classes.

Definitions specific to this category can be found in Definitions/Differentiability Classes.

Let $f: \R \to \R$ be a real function.

Then $\map f x$ is of **differentiability class** $C^k$ if and only if:

- $\dfrac {\d^k} {\d x^k} \map f x \in C$

where $C$ denotes the class of continuous real functions.

That is, $f$ is in **differentiability class $k$** if and only if there exists a $k$th derivative of $f$ which is continuous.

If $\dfrac {\d^k} {\d x^k} \map f x$ is continuous for all $k \in \N$, then $\map f x$ is of **differentiability class** $C^\infty$.

## Subcategories

This category has only the following subcategory.

### E

## Pages in category "Differentiability Classes"

The following 5 pages are in this category, out of 5 total.

### D

- Derivative Operator is Linear Mapping
- Derivative Operator on Continuously Differentiable Function Space with C^1 Norm is Continuous
- Derivative Operator on Continuously Differentiable Function Space with Supremum Norm is not Continuous
- Differentiability Class is Subset of Differentiability Class of Lower Order