# Chain Rule

(1.4 hours to learn)

## Summary

The chain rule for partial derivatives gives a way of computing the partial derivatives of compositions of functions in terms of the partial derivatives of the individual functions.

## Context

This concept has the prerequisites:

- partial derivatives (The chain rule is a way of computing partial derivatives.)
- linear approximation (The idea of linear approximation explains why the chain rule works.)
- matrix multiplication (The chain rule formula involves a matrix multiplication.)

## Goals

- Know the statement of the chain rule (in matrix form)

- Be able to use it to compute partial derivatives

- Understand the justification in terms of linear approximations of functions

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

## -Free-

→ MIT Open Courseware: Multivariable Caclulus (2010)

Video lectures for MIT's introductory multivariable calculus class.

## -Paid-

→ Multivariable Calculus

An introductory multivariable calculus textbook.

Location:
Section 13.7, "The multivariable chain rule," pages 896-904

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 3.3, "Differentiation rules," pages 97-102

## See also

-No Additional Notes-