Hello I am trying to figure out what is the growth rates for some fucntions.

So far I only know the order for the basic functions but I would also like to know where would some special/different fucntions would fit

From textbook:

Constant, logN, logn^2, N, NlogN, N^2, N^3 and 2^N (right side growing the fastest)

I would like to know where would the following fucntions fit

N^(1/2), loglogN, N / logN, (1/3)^N, (3/2)^N

Here is my guess,

When N is small such as using N=2

Constant, loglogN, N, N^(1/2), logn^2, logN, N, NlogN, (1/3)^N, (3/2)^N, N / logN

When N is a large number such as N=333

Constant, loglogN, logN, logn^2, NlogN, (1/3)^N, N^(1/2), N, (3/2)^N, N / logN

A guess with out plugging in numbers for N

Constant, loglogn, logn, logn^2, n^(1/2), n, nlogn, (1/3)^n, (2/3)^n, n/logn

This is how I came to my guess, I tried plugging in numbers into N for each fucntion and look at their results. However I got different results of growth order when I used different numbers. I used 2 and 333 for N. Some fucntions grew much faster with a bigger N than with a smaller. I am not sure how to figure out my problem.

Thanks for your help!