# partial derivatives

(1.1 hours to learn)

## Summary

"A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary)" [wikipedia entry]. Intuitively, a partial derivative measures the instantaneous rate of change for a single variate in a multivariate function.

## Context

This concept has the prerequisites:

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

Location:
Session 26, "Partial derivatives"

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 13.4, "Partial derivatives," pages 868-875

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 3.1, "Partial derivatives and directional derivatives," pages 81-85

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Wikipedia

→ Wolfram MathWorld

## See also

- Higher order partial derivatives
- Partial derivatives can be used to compute:
- the gradient , an operator which "points uphill"
- directional derivatives , which compute the rate of change with respect to movement in a particular direction