This next question is more involved – don’t take the long difficult route.

In this example (see below) I demonstrate how you can greatly simplify a problem by considering connecting three rates of change instead of two. (1st video) In the second video I do the question again but just combine the usual two rates of change so that you can compare two methods. I think you will agree that the first is a lot easier.

Example:

A spherical balloon is being inflated by helium at a steady rate of 150 cm^{3} s^{-1}. Find the rate of change of the surface area when the radius is 6 cm.

Best Method

Alternative method but very slow – I would not advise it.