Overview
The derivative tells us how a change in one variable affects another variable. Related rates problems ask how two different derivatives are related. For example, if we know how fast water is being pumped into a tank we can calculate how fast the water level in the tank is rising. The chain rule is the key to solving such problems.
Lecture Video and Notes
Video Excerpts
» Clip 1: Introduction to Related Rates (00:05:00)
From Lecture 12 of 18.01 Single Variable Calculus, Fall 2006
» Clip 3: Rates: A Conical Tank (00:13:00)
From Lecture 13 of 18.01 Single Variable Calculus, Fall 2006
Recitation Video
Inflating a Balloon
> Download from iTunes U (MP4 - 17MB)
> Download from Internet Archive (MP4 - 17MB)
Sliding Ladder
> Download from iTunes U (MP4 - 38MB)
> Download from Internet Archive (MP4 - 38MB)
Worked Example
Solving an Optimization Problem Using Implicit Differentiation