The first type of function that we differentiate will be powers of x. [br][br]If attempting to prove these results (not done in this activity) we often begin by looking at positive integer powers and these are the first functions we may consider. [br][br]However, the rule works for negative and fractional powers of x as well.[br][br]Start by seeing if you can apply the rule to positive integer powers of x. Try to evaluate the derivative for different functions (change a and n with the sliders) and then check your answer.[br][br][i][You can change the coordinates of the x-axis by changing x_min and x_max][/i]

Now use the following activity to notice that the same rule applies when working with negative integer powers.

Now try different (non-integer) values of [i]n[/i] and see if you can correctly predict the derivative.