Presumably, the limit is
Now, if you're familiar with the definition of the derivatives, you'll notice that this is the limit form of the derivative of the function
, which you may also know to be
. But let's assume you don't know that just yet, and that it's actually the result you intend to find.
Expand the numerator:
Now, when
, we can divide through by the lowest power of
. We can do this because we're considering the limit as
is *approaching* 0, and not when it actually takes on the value of
.
Now, as
, we can see only the leading term remains, so that
as expected.