We often have to differentiate polynomials. For polynomials of the formit is as simple as multiplying by the power and subtracting one from the power.

Example:

This extends to multiples and sums of powers ofIf we remember thatand that when differentiating for these functions too we multiply by the power and subtract one from the power then,

The process is the same for all powers offractions and negative powers included:

Whatever form the question is given it we must expression the function to be differentiated in the formFor example,

We write this as then

These are some more examples,

Differentiation is used to find rates of change (when we differentiate with respect to time), gradients, slopes, tangents and normals.