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

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.