### Introduction

We have seen, in the first three Sections, how standard functions like ${x}^{n}$ , ${e}^{ax}$ , $sinax$ , $cosax$ , $lnax$ may be differentiated.

In this Section we see how more complicated functions may be differentiated. We concentrate, for the moment, on products and quotients of standard functions like ${x}^{n}{e}^{ax}$ , $\frac{{e}^{ax}lnx}{sinx}$ .

We will see that two simple rules may be consistently employed to obtain the derivatives of such functions.

#### Prerequisites

- be able to differentiate the standard functions: logarithms, polynomials, exponentials, and trigonometric functions
- be able to manipulate algebraic expressions

#### Learning Outcomes

- differentiate products and quotients of the standard functions
- differentiate a quotient using the product rule