By Eric Lake

This module both has video lectures and also a worksheet with practice problems below!

This is an introduction to the Product Rule, with an example to show we cannot split derivatives across multiplication.

Here is a classic example that utilizes the Product Rule.

In this video, I go through the product rule way of doing this problem, as well as FOILing and using the power rule, like we did in 3.1.

In this problem, we change e^2x into a product so we can use the product rule to evaluate it.

This video shows the Quotient Rule, and does a problem with it, as well as verifies the result using 3.1 methods.

In this example, we have to solve it with the Quotient Rule!

For this example, though we can do the Quotient Rule, there is an easier way to do it! Just pull out the constant out front.

This problem looks easy because its numerator is easy, but because its denominator has two terms, we must evaluate with the Quotient Rule.

This Quotient Rule problem requires us to use the Product Rule on one of the derivatives!

In this problem, we don't have two things multiplied, but three things multiplied! We do this by using the Product Rule repeatedly.

In this problem, we only know f and g and its derivatives at a single point. We can still use the product and quotient rule to evaluate these!

For your practice, here is a worksheet on several problems on the Product and Quotient Rules. Do your best to do these without looking notes or a video, at least until you get stuck, then take a look at those resources.

When you are finished, check your work with the full worked solutions.