Derivative of $n^{\log n}$? What would be the derivative of $n^{\log n}$? I have to prove that $(\log n)^n$ = $\omega$($n^{\log n}$). I am trying to implement L'Hopital rule.

Put $y = n^{log n} $
$$\implies \log y = \log n \log n \implies \frac{y'}{y} = \frac{\log n}{n} + \frac{ \log n}{n} = \frac{2 \log n}{n}  $$
$$ y' = \frac{y 2 \log n}{n} \implies y' = \frac{2 n^{\log n} \log n}{n} $$
