## Differentiation

**Differentiation gives the**

__gradient of a curve__for any point on it, which also shows the__rate of change__between two valuesGiving:

When differentiated:

y = 2x becomes

f(x) = 2x becomes f'(x) = 2

y = 2x becomes

__dy__= 2**dx**f(x) = 2x becomes f'(x) = 2

**E.g.**

## Second Order Derative

**Differentiate Twice**

## Differentiation and Straight Lines

The

By putting it into the equation and substituting in the

**differentiated value**can be put into the straight line equation as the**gradient**allowing for the**equation for the tangent and the normal**at a point on the curve to be found outBy putting it into the equation and substituting in the

**x and y**co-ordinates**can be found out algebraically. Allowing for the equation for the line to be discovered**__c__