# Smoothness

## Number of derivatives of a function (mathematics) / From Wikipedia, the free encyclopedia

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In mathematical analysis, the **smoothness** of a function is a property measured by the number, called *differentiability class*, of continuous derivatives it has over its domain.^{[1]}

A function of **class** $C^{k}$ is a function of smoothness at least k; that is, a function of class $C^{k}$ is a function that has a kth derivative that is continuous in its domain.

A function of class $C^{\infty }$ or $C^{\infty }$-function (pronounced **C-infinity function**) is an **infinitely differentiable function**, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous).

Generally, the term **smooth function** refers to a $C^{\infty }$-function. However, it may also mean "sufficiently differentiable" for the problem under consideration.