What exactly is the Derivatives folder?

Rule number one: there are no user-serviceable parts within the library package, and changing anything there can cause dataloss.

The app has several different versions of the photograph: the original, the Preview (used in the sharing mechanism) but also versions that are scanned for the faces and for object identification. Not sure what exactly the derivatives folder is for, but it's part of the library and so rule number one applies.

I know nothing about this, except you're not supposed to go mucking around inside the Photos Library package. However, it seems that the Derivatives folder belongs inside the Resources folder inside the library package. The contents seem to be medium resolution versions (1024 x 768, for example) of cropped pictures. Perhaps this is used for making thumbnails and for full screen viewing?

When I search for the picture whose derivative I was looking at, it appears not to be in the Library at all. This is a small test library, small enough that I can look through the whole library. Hold it-- it's in recently deleted. Hmm.

Resources and Derivatives should be inside the Photos Library package. If they are outside, they may be parts of a damaged Photos Library. This can happen, if you are trying to keep a Photos Library in a synced folder, for example in a Dropbox. Or if you try to Trash a pHotos Library and the Trash cannot be emptied properly.

If it is inside the Photos Library package, we can't say, since it is probably some Apple Photos Database Juju. While their some documented ways to access Photos internals, we don't know the details on those internals.

If it is *outside* the package, you need to find out who created the folder.