
Differentiating Powers
On this page, we will introduce the
Power Rule
In fact, we have already seen an easy example of this when
that is, we saw that
To see how the power rule works in another case, let's consider
by applying the product rule.
Notice that
which agrees with the power rule, as stated above, when
In the same way, we can compute that
which again agrees with the power rule.
Example:
The Power Rule tells us that the derivative
Below, the graph of the function
is shown on the left while its derivative
is shown on the right.
Questions:
 Can you explain the relationship between these
two graphs?
 What can you infer from the fact that the derivative is
always positive?
 What happens at the point where the
derivative is equal to zero?


