Prove that $$n^\frac{1+2}{\sqrt{\log n}} = O(n\ \log n).$$

I want to compute the two growth rates by using L'Hôpital's rule: 

$$\lim\_{n\to \infty} \frac{f(n)}{g(n)}$$

so I get something like this: 

$$\lim\_{n\to \infty}\frac{n^\frac{1+2}{\sqrt{\log n}}}{n\ \log n}$$

However the main trouble I'm having is differentiating $$ n^\frac{1+2}{\sqrt{\log n}}$$

What would be the best way to approach $f(n)$? 

Thanks in advance, guys.