### Introduction

When one variable is related to several others by a functional relationship it is possible to estimate the percentage change in that variable caused by given percentage changes in the other variables. For example, if the values of the input variables of a function are measured and the measurements are in error, due to limits on the precision of measurement, then we can use partial differentiation to estimate the effect that these errors have on the forecast value of the output.

#### Prerequisites

- understand the definition of partial derivatives and be able to find them

#### Learning Outcomes

- calculate small errors in a function of more than one variable
- calculate approximate values for absolute error, relative error and percentage relative error

#### Contents

1 Approximations using partial derivatives1.1 Functions of two variables

1.2 Functions of three or more variables

2 Engineering Example 2

2.1 Measuring the height of a building

3 Relative error and percentage relative error

4 Engineering Example 3

4.1 Error in power to a load resistance