---
tag: 0HHHDCXZV4
kind: concept
name: Differentiable function of several variables
aliases: [differentiable-map, totally-differentiable-function]
msc: [26B05]
uses: [0FNKFT8H6E, 0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Differentiable_function
    locator: Differentiability in higher dimensions
---

## Summary

A function of several variables is differentiable at a point when, near that point, it is close to a linear function plus a constant. The error is small compared with the distance to the point.
The linear function is the [[total derivative|0FNKFT8H6E]] of the function at the point.