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Derivatives: How to Find
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The Basic Rules of
The Power Rule
Here is one of the most basic rules of calculus, perhaps the single rule that more people think of
when someone says, ``What do you remember from calculus?" Besides, it has that great name,
The Power Rule.
It says:
Now what does that mean? Well,
n
can be any number. So if we let
n
be 3, we have:
If we let
n
be 5, we have:
If we let
n
be 1, we have:
This is worth remembering separately, so let's repeat it so it sticks:

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We could also let
n
be a negative number. For instance, if
n
=-2, we have
Notice that we can now take the derivative of 1/
x
:
In fact,
n
can even be a fraction. So for instance, we can take the derivative of
, since:
The fact that
n
needn't be a whole number usually doesn't get mentioned in this part of a course
on calculus, but we'll clue you in a little early. That little
n
could even be a number like
or
.
Then:
We know it's tempting to try to simplify the exponent

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