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.

Note that $f(x)=x^{\log x}=e^{(\log x)^2}$. By the chain rule, the derivative is
$$f^\prime(x)=\frac{2\log x}{x} e^{(\log x)^2}=\frac{2\log x}{x} x^{\log x}$$
