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.