---
tag: 09EGC6F8PT
kind: concept
name: Partial derivative
aliases: [partial-derivatives]
msc: [26B05]
uses: [0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Partial_derivative
    locator: lead section
same_as:
  wikidata: Q186475
  wikipedia: Partial derivative
---

## Summary

A partial derivative of a [[function of several variables|0JPCHTXWG0]] is its derivative with respect to one variable, while all other variables stay fixed.
It measures the rate of change of the function along one coordinate axis.
For $f(x, y) = x^2 y$, the partial derivatives are $\partial f / \partial x = 2xy$ and $\partial f / \partial y = x^2$.