# Smoothness

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

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Smooth function?

Summarize this article for a 10 years old

SHOW ALL QUESTIONS

In mathematical analysis, the **smoothness** of a function is a property measured by the number of continuous derivatives it has over some domain, called *differentiability class*.[1] At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous).[2] At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be **infinitely differentiable** and referred to as a **C-infinity function** (or $C^{\infty }$ function).[3]

Number of derivatives of a function (mathematics)