Compare functions

Question

Could you please check if I correctly compared functions? I used basic theorems about big-O notation:

$$ \ln(\ln(n))<\log_2(n^n)<\ln^2(n)<(\log_2 (n))^n<5n \log_2 (n)<(n+1)^2<n^{\ln(n)}<n^n<2^{2^{n}}$$

$\ln(n)$ is the natural log of $n$.