Related rates
image by gehat
image by gehat

Related rates problems comprise one of the many applications of the derivative. This technique is used in problems involving changing variables. Our goal is to find an equation to relate the two changing variables to each other, so that we may solve the given problem. Most of the time, the change is with respect to time, though be aware that this is not always the case. Before attempting to do problems involving related rates, it is important to understand the derivative rules, particularly those concerning implicit differentiation.

Common related rate scenarios include inflating balloons, moving cars and planes, and filling/emptying geometrically shaped containers.

Sorry, but these are usually word problems, which means that you have to read, and read carefully!! Here are some handy formulas and examples for you to look at to show you what it's like.

Handy Formulas

Related Rates Problem

Another Related Rates Problem

Try these problems on your own.

Problem #1:
Problem #2:

Answer WAY below

Answers for #1:

Answers for #2: