remember, to apply L'Hospital's Rule you need
lim x --> c where f(x) and g(x) are some function dependent on x. Furthermore, lim f(x) and lim g(x) both must be either 0 or +- infinity. This mear fact tell you that, you want to have a fraction of two function with x on numerator and denominator such that both have limit or either 0 or +- infinity.
once that is done, following holds:
lim x -> c lim x -> c
so what i'm trying to tell you here is this:
a) you want to have numerator and a denominator dependence on x. So, i would start by taking common denominator to get something of the form f(x) / g(x)
a) you want to make sure both lim f(x) and lim g(x) go to 0 or +- infinity before you use L'Hospital's Rule. So, taking derivative as you did is irrelevant when you clearly don't have a single numerator and a denominator and neither they go to 0 or +- infinity in given form.