In this section, we will investigate how to take the derivative of the product or quotient of two functions.

Section 3.1 Product Rule & Quotient Rule

TheoremProduct Rule of Derivatives

Suppose . Then:

Note, this is very different than , which is not correct.

Example 1

Find the derivative of the function .

Example 2

Find the derivative of the function .

Example 3

Find the derivative of the function .

TheoremQuotient Rule of Derivatives

Suppose . Then:

Note, this is very different than which is not correct.

Example 4

Find the derivative of the function .

Example 5

Find the derivative of the function .

Example 6

Find the derivative of the function .

Example 7

Use the quotient rule to prove .

Example 8

Use the quotient rule to prove .

Suggestion

In a similar way we can prove the two derivatives shown below. I suggest you work on this sometime.

Example 9

Show that by taking the derivative of F.