Category:Differentiability Classes

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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 $C^\infty$.