When trying to derive a function that has two values multiplied together, we use the product rule.

This can be shown by the following formula:

This simply shows that to derive u × v, you simply derive them separately. Once you’ve done this, you multiply each of these values by the others original value, and then add them together.

Here’s a worked example:

Of course in this instance the product rule is not needed, and can also be solved the following way:

This does however prove that the product rule works, and In other instances, where the value cannot be simplified before deriving it, it is needed.