Hello. Here is an overview of the product rule from calculus. 

<center><img src="https://study.com/cimages/course-image/clep-calculus-course_128015_small.jpg" /></center>
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It is assumed that the reader knows what a calculus derivative is and is familiar with derivatives of functions such as http://quicklatex.com/cache3/c9/ql_a9e6c70ccef3cab0b31eef38422933c9_l3.png, http://quicklatex.com/cache3/11/ql_8a4ff3d4f9b021dd25f544a1dcf1b811_l3.png and so on.

(Math text, symbols are done in LaTeX and converted into images with QuickLaTeX.com)



### The Product Rule
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The product rule is used when you want to take the derivative of one function `f(x)` multiplied by another (different) `g(x)` function. We have:

<center>http://quicklatex.com/cache3/c7/ql_4f8a47d175177e081c4b394498eb6cc7_l3.png</center>

The derivative of `h(x)` is `h'(x)` and the form is as follows:

<center>http://quicklatex.com/cache3/cb/ql_00700124cf16de0c3d602220987368cb_l3.png</center>

Think of the derivative `h'(x)` in as the derivative of the first multiplied by the second function + first function multiplied by the derivative of the second function.

### A Memory Aid For Product Rule
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There is a neat memory aid for the calculus product rule. Instead of using the argument `x` in `f(x)`, I use just `f` and `g` from `g(x)`.

Instead of http://quicklatex.com/cache3/cb/ql_00700124cf16de0c3d602220987368cb_l3.png, an easier way is to use http://quicklatex.com/cache3/1a/ql_4493997d9e3a39f6c7db20a2b93fc11a_l3.png.

### Examples of Product Rule
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**Example One**

Suppose that http://quicklatex.com/cache3/8f/ql_149491cc17d8322ffd0710fba32a538f_l3.png and `h(x)` is in the form of http://quicklatex.com/cache3/cf/ql_96b49787ba49d37438913e1e1f1659cf_l3.png.

Here we have `f(x) = x` with `f'(x) = 1`.

and http://quicklatex.com/cache3/d2/ql_973fb1012b939ea0b653a9e200a32cd2_l3.png with http://quicklatex.com/cache3/ee/ql_c4d16f12d9593945b3c17f580b8021ee_l3.png.

Substituting the components into the product rule formula would give `h'(x)` as:

<center>http://quicklatex.com/cache3/de/ql_55909cef2ab685de697afd0e9e6f56de_l3.png</center>

**Example Two**

What is the derivative of http://quicklatex.com/cache3/2f/ql_a2210f70936bd649177dd79981388a2f_l3.png? 

The product rule formula would give `h'(x)` as:

<center>http://quicklatex.com/cache3/c1/ql_dd15a7ee09c6d4603ecda05791898ac1_l3.png</center>


**Example Three**

Determine the derivative of http://quicklatex.com/cache3/96/ql_a9265dc506a0258cfa58480740f72c96_l3.png.

With the product rule formula, this would give:

<center>http://quicklatex.com/cache3/c0/ql_777a0981f323703071c1b6b16970dfc0_l3.png</center>


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