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. $y=f\left(x\right)$
• 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