I have two functions:

$\displaystyle f(n)=3^\log_{2}n^2$

and

$\displaystyle g(n)=3^\log_{2}\frac{n^2}{2}$

I have to prove it its big-Oh/theta/omega

I have to use the limit method where:

limit n going to infinity of

$\displaystyle \frac{f(n)}{g(n)}$

Then L'Hospital's rule, but when I take the derivatives of both and cancel out everything I just get what I was left with before. Am I doing something wrong? Am I not taking the derivative correctly?

I was using $\displaystyle \frac{d}{dx}a^x=log(a)a^x$ and chain rule.

Can someone help me to clarify this?