### Lecture Description

In this video lecture, Prof. Gilbert Strang discusses Chains f(g(x)) and the Chain Rule.

A chain of functions starts with y = g(x). Then it finds z = f(y). So z = f(g(x)). Very many functions are built this way, g inside f . So we need their slopes.The Chain Rule says: Multiply the Slopes of f and g.Find dy/dx for g(x). Then find dz/dy for f(y).Since dz/dy is found in terms of y, substitute g(x) in place of y.The way to remember the slope of the chain is dz/dx = dz/dy times dy/dx.Remove y to get a function of x. The slope of z = sin (3x) is 3 cos (3x).

### Course Index

- Faculty Introduction
- Big Picture of Calculus
- Big Picture: Derivatives
- Max and Min and Second Derivative
- The Exponential Function
- Big Picture: Integrals
- Derivative of sin x and cos x
- Product Rule and Quotient Rule
- Chains f(g(x)) and the Chain Rule
- Limits and Continuous Functions
- Inverse Functions f ^-1 (y) and the Logarithm x = ln y
- Derivatives of ln y and sin ^-1 (y)
- Growth Rate and Log Graphs
- Linear Approximation/Newton's Method
- Power Series/Euler's Great Formula
- Differential Equations of Motion
- Differential Equations of Growth
- Six Functions, Six Rules, and Six Theorems

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The series is divided into three sections:

**Introduction**

- Why Professor Strang created these videos

- How to use the materials

**Highlights of Calculus**

- Five videos reviewing the key topics and ideas of calculus

- Applications to real-life situations and problems

- Additional summary slides and practice problems

**Derivatives**

- Twelve videos focused on differential calculus

- More applications to real-life situations and problems

- Additional summary slides and practice problems

**Acknowledgements**

Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.