## Learn about the product rule - when to use it and why

Given a function , how would you differentiate the function?

Differentiating it with the definition would be quite a chore. Just try expanding ...

Well, is the product of two functions, and , right?

Now think about what the derivative represents. The derivative describes a rate of change. How does the product change?

If we increase by some small quantity , it will cause a change in as well as in . The changes in the composite functions in turn depend on and . So we'd expect the terms and to crop up somewhere.

Since we're dealing with a product, it'd also be logical if there was some multiplication going on here.

Thus, the rule for the derivative of a product is:

It appears all the time, so you should be able to give the right answer.

Since:

then we get:

The product rule ## Good outline for calculus and short to-do list

We work hard to provide you with short, concise and educational knowledge. Contrary to what many books do. ## Get exam problems for old calculus exams divided into chapters

The trick is to both learn the theory and practice on exam problems. We have categorized them to make it extra easy.