### Introduction

In this Section we will see how to obtain the derivative of a composite function (often referred to as a ‘function of a function’). To do this we use the
**
chain rule
**
. This rule can be used to obtain the derivatives of functions such as
${e}^{{x}^{2}+3x}$
(the exponential function of a polynomial);
$sin\left(lnx\right)$
(the sine function of the natural logarithm function);
$\sqrt{{x}^{3}+4}$
(the square root function of a polynomial).

#### Prerequisites

- be able to differentiate standard functions
- be able to use the product and quotient rule for finding derivatives

#### Learning Outcomes

- differentiate a function of a function using the chain rule
- differentiate a power function

#### Contents

1 The meaning of a function of a function2 The derivative of a function of a function

3 Power functions