A "derivative work" is any song that takes a preexisting work and uses that material to create a new composition. It differs from a cover song, which is a more straightforward interpretation of an existing composition without significant alterations to the melody or lyrics.
In music, examples of derivative works include:
- language translations
- samples or replaying (re-recording a segment of the original song)
- songs arrangements that change lyrics, abridge the music or make other significant alterations to the original composition.
You CANNOT distribute a derivative work without the permission of the copyright holder of the pre-existing work. Unlike cover songs, the copyright holder CAN deny you permission to create a derivative work for any reason.
If a derivative work has been properly licensed with permission from the original publisher or copyright holder, you can distribute that song as an original work with the proper songwriting ownership of the new song listed. That ownership should reflect the license you have negotiated with the creator of the work you created a derivative work from.