Product and Quotient Rules

for Derivatives

 

The product rule and quotient rule are repeated here for convenience.

 

Review the words associated with these rules in the previous lecture.

We now work some example problems using these rules alone and also combine them with the pervious rules. You should work your problems using the same steps that I use here. The first step in using the product or quotient rule must be the same as I have here. The formula must first be written down with the relevant functions without doing anything else. Consider the following example.

Notice very carefully that in the first step I wrote down just the rule using the functions given in this problem. Even though in the first step I knew the derivatives of the two elementary functions I did not use this information at this time. The first step is to write down the relevant rule and do nothing else. This is how to learn the rules. You have no choice, you must do it this way. That's what I'm teaching, that's what you should be learning and that's what you will be tested on. If you don't do it consistently on you homework you might forget to do it on the test. You can not then say that you know how to do it but forgot to do it because that's what the test will be; for you to do it this way. Make sure that you understand this. The last step, rearranging, is not relevant.

Examples

Product rule.

 

Quotient rule.

 

Now we mix several of the rules together.

 

 

You should become very comfortable with taking the first step exactly as I did in each and every example.

Homework

Product rule.

 

Quotient rule.

 

Mixture of several rules.

 

Answers

Product rule # 1 - 5 with work.

Quotient rule # 6 - 10 with work.

Mixture of several rules # 11 - 14 with work. (# 14 partial, finish below)

Mixture of several rules continued # 14 finished and # 15.