Where can/should I, as a high schooler, publish a paper regarding the derivation of a formula?
The big question here is whether what you've done is new to the world - whether it's a genuine new advance that nobody in the world has done before, or whether it's something known to the world that you, and perhaps your teacher, have not seen before. Without meaning any disrespect to you and your friend, the second option here is more likely - but the first is of course possible. 

If it's genuinely new, you can look to publish in a scientific journal. If it's not new (but perhaps still unusually advanced for a high school student), you should perhaps look for other types of publication, which could still be good for your resume. The difficult question is how to tell which category your work falls into.

My suggestion is to speak to your high school teacher about this. They have seen a lot of different students' work. If they think that it may be a novel development, then either write, or get your teacher to write, to a professor in a relevant subject at a local university. See if they will look it over and advise you.