# Calculus

Calculus helps us to understand the gradient of a curve.

## Gradient function

The derivative gives us a ‘gradient function’ i.e. a formula that will give the gradient at a point on the curve.

The gradient on a curve is different at different points on a curve.

On this graph:

When the gradient is positive.

When the gradient is equal to zero.

When the gradient is negative.

## Differentiation

To find the gradient function (derivative) for a model or graph we differentiate the function. The technique of differentiation can be carried out using algebraic manipulation.

Find out more about algebraic manipulation such as rearranging equations and the law of indices.

In general : For the function then

Khan academy step though this power rule with a number of examples.

*e.g.*

then

The following video will take you through three more examples of differentiating polynomials.

Practice this technique on Khan Academy. Hints and further videos are available.

## Notation

There are three commonly used notation methods for the derivative of a function.

If then | is the derivative of with respect to |

If then | is the gradient function of |

If we differentiate with respect to we get |