Should I apologize to my coauthors for being slow to finish a paper draft? I am first author on a paper about my research from last summer.  Due to a busy school year and a bout of severe depression, I have taken FAR longer to finish this paper than originally planned.  

When I send the draft to my coauthors, should I apologize?  Thank them for their patience?  Promise to be better in the future?

As a very young researcher, my primary concern is seeming professional and reliable to my coauthors.
Delays on this sort of thing are extremely common.  So, unless there is some specific reason that this work is time sensitive, it's unlikely that anybody is going to be surprised or upset by this: don't worry too much about it.  Certainly, don't beat yourself up about it, especially when you had legitimate reasons for the delay.

That said, a brief apology is a good idea.  All you need is something like:


  Sorry for the delay with this; the last few months have been really hectic.


Don't make too much of it; just acknowledge the delay and move on.