### Introduction

Differentiation is a technique which can be used for analysing the way in which functions change. In particular, it measures how rapidly a function is changing at any point. In engineering applications the function may, for example, represent the magnetic field strength of a motor, the voltage across a capacitor, the temperature of a chemical mix, and it is often important to know how quickly these quantities change.

In this Section we explain what is meant by the gradient of a curve and introduce differentiation as a method for finding the gradient at any point.

#### Prerequisites

- understand functional notation, e.g. $y\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}f\left(x\right)$
- be able to calculate the gradient of a straight line

#### Learning Outcomes

- explain what is meant by the tangent to a curve
- explain what is meant by the gradient of a curve at a point
- calculate the derivative of a number of simple functions from first principles

#### Contents

1 Drawing tangents2 Finding the gradient at a specific point

3 Finding the gradient at a general point

4 Differentiation of a general function from first principles