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.