---
tag: 06KWGHDN2J
kind: concept
name: Directional derivative
aliases: [gateaux-derivative-in-a-direction, line-derivative]
msc: [26B05]
uses: [09EGC6F8PT]
sources:
  - url: https://en.wikipedia.org/wiki/Directional_derivative
    locator: lead section
same_as:
  wikidata: Q383851
  wikipedia: Directional derivative
---

## Summary

The directional derivative of a function $f$ at a point $a$ in the direction of a vector $v$ is a rate of change. It is the rate of change of $f$ when its input moves from $a$ along $v$.
It is the derivative at $t = 0$ of the function $t \mapsto f(a + t v)$ of one variable.
The [[partial derivatives|09EGC6F8PT]] are the directional derivatives along the standard basis vectors.