We often have to differentiate functions. For functions of the form
it is as simple as multiplying by the power and subtracting one from the power.
Example:
This extends to multiples and sums of powers of
If we remember that
and 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 of
fractions and negative powers included:
Whatever form the question is given it we must expression the function to be differentiated in the form
For 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.