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# Derivatives: Product, Quotient, and Chain Rules

Author: c o
##### Description:

To introduce the product rule, quotient rule, and chain rule for calculating derivatives
To see examples of each rule
To see a proof of the product rule's correctness

In this packet the learner is introduced to a few methods by which derivatives of more complicated functions can be determined.

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Tutorial

## Introduction

Before starting with this packet, you should be comfortable with the concept of a derivative of a function.

You will need to know how to find the derivative of powers of x and of the sine function, for your convenience, the shortcuts follow: # Introduction

Often we are able to write a function as a kind of combination of two simpler functions, and when we can, we'd like to know how this affects the derivative.  An example of such a function might be f(x) = 2x2sin(x), which could break down into component functions like this: g(x) = 2x2, h(x) = sin(x) so that f(x) = g(x)h(x).

But how do we calculate the derivative of such a function? It turns out that mathematicians have discovered rules that help to simplify this task.  This packet states and gives examples of these rules, and even proves why one of them works.

# The Rules

The Product Rule The Quotient Rule The Chain Rule And now for some examples.

## Examples

In this video we see an example of each of the Product Rule, the Quotient Rule, and the Chain Rule.

## Proving The Product Rule

In this video we apply our knowledge of the definition of the derivative to prove the product rule.

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