Here is a quick lesson covering the Product Rule, and the Quotient Rule in Calculus.

**Prerequisite**

This lesson assumes that the student knows what a calculus derivative is and is familiar with derivatives of functions such as , and so on.

**Product Rule**

The product rule is used when you want to take the derivative of one function multiplied by another (different) function . We have:

**(1.1) **

**(1.2)**

**(1.3)** (derivative of the first multiplied by the second function) + (first function multiplied by the derivative of the second function)

__Example of Product Rule__

Suppose that and is in the form of .

Here we have with

and with .

Substituting the components into the product rule formula in **(1.2)** would give as follows:

**Quotient Rule:**

The quotient rule is similar to the product rule but it has more steps. It is used when you want to take the derivative of one function **divided** by another (different) function . We have:

**(2.1) **

**(2.2)**

**(2.3)**

( (derivative of the first multiplied by the second function) – (first function multiplied by the derivative of the second function)) DIVIDED BY (second function squared)

__Example of Quotient Rule__

Suppose that and is in the form of .

Here we have with

and with and .

Substituting the components into the quotient rule formula in **(2.2)** with some factoring and simplifying would yield:

or .

**An Easy Way To Remember Product and Quotient Rule:**

I personally use this memory trick often for both product rule and quotient rule. Instead of using the argument in , I use just .

Instead of , an easier way is to use .

For the quotient rule it would be: .

Note that when using the shorthand notation, one should know what the independent variable is. In this case, it would be .