This question is closed as being opinion-based. Perhaps I do not understand English well, could someone explain in more detail what opinion-based is on this question?
1) Is this derivation correct?
Check-my-work questions are generally off-topic here.
2) Does this form have some physical interpretation?
This is a fairly broad question. What type of physical interpretation are you looking for? Additionally this is somewhat opinion based, as different people will have different ideas as to what constitutes a "physical interpretation". For example, is entropy physical, or is it just a really useful tool in statistical mechanics? I am sure you would get a wide variety of opinions on this point.
3) Is this a useful formula for calculating some physical value?
If something is "useful" or not is subjective. And once again, "some physical value" is pretty vague.
Additionally, posts that ask multiple questions are also considered to be off-topic for this site.
Therefore, your post has many problems as it stands; it is a subjective, unclear, unfocused, check-my-work question. Since there can only be one close reason reported in the close banner (I think?), I am sure one was chosen from the list. However, this is not anything against you, and you can easily fix this. As an additional bonus, since there are no answers on the question currently, you can get away with largely editing the question and getting it reopened if you want to. Or, you can just ask a new, better question that is objective and more focused on physics concepts rather than a computation. I would suggest looking at the FAQ as well as the help center to learn more about what types of questions are/are not on-topic for this site.
A commenter writes
I would not have picked opinion-based, but would have voted to close (although answering question 2 is opinion based). Too broad (3 questions), homework like (1st question), just not a good fit.
I was the one who closed the question, and that's exactly what I was thinking. Not a good fit, for multiple reasons. See the help center for guidance on getting the community to possibly re-open your question.