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.