Highlights of Calculus

Highlights of Calculus (Res.18-005, MIT OCW). Instructor: Professor Gilbert Strang. 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: 1) Introduction - Why Professor Gilbert Strang created these videos, 2) Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus, Applications to real-life situations and problems, and 3) Derivatives - Twelve videos focused on differential calculus, More applications to real-life situations and problems. (from

Lecture 08 - 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).

Go to the Course Home or watch other lectures:

Highlights of Calculus (5)
Lecture 01 - Big Picture of Calculus
Lecture 02 - Big Picture: Derivatives
Lecture 03 - Max and Min and Second Derivative
Lecture 04 - The Exponential Function
Lecture 05 - Big Picture: Integrals
Derivatives (12)
Lecture 06 - Derivative of sin x and cos x
Lecture 07 - Product Rule and Quotient Rule
Lecture 08 - Chains f(g(x)) and the Chain Rule
Lecture 09 - Limits and Continuous Functions
Lecture 10 - Inverse Functions f-1(y) and the Logarithm x = ln y
Lecture 11 - Derivatives of ln y and sin-1(y)
Lecture 12 - Growth Rate and Log Graphs
Lecture 13 - Linear Approximation/Newton's Method
Lecture 14 - Power Series/Euler's Great Formula
Lecture 15 - Differential Equations of Motion
Lecture 16 - Differential Equations of Growth
Lecture 17 - Six Functions, Six Rules, and Six Theorems