First, a derivative is a work based on preexisting material, where enough new creative and original material has been added to make the resulting work eligible for copyright protection. Making derivatives is one of the
exclusive rights held by a copyright holder so if someone wants to base a new work on the original, they will (generally) need to get permission from the copyright holder to do this.
With a public domain work, however, anyone is free to use the original work, so no permission is needed from the copyright holder. Any derivatives made of the public domain work, however, will have elements that can be protected under the copyright law. To use a derivative of a public domain work would require permission of the copyright holder. An example of a derivative of a public domain work would be Ted Turner's colorized versions of public domain black-and-white films. The black-and-white films can be used by anyone but the colorized versions are copyright-protected and would require permission from Turner.
The original blues version of "When the Levee Breaks" as written by Memphis Minnie is in the public domain. Led Zeppelin took the original version of the public domain song and changed the lyrics a bit and changed the tempo or cadence of the music. They added the drums and harmonica. The derivative created by Led Zeppelin of the original Memphis Minnie version, with its original and creative elements added to the original, is copyright-protected. To use the Zeppelin version, licensing is required.
There are numerous licensed covers of the Zeppelin version by various and assorted artists which might make it seem that the Zeppelin version is the original Memphis Minnie version, but it isn't. The Memphis Minnie version with its lyrics and music can be used by anyone. Zeppelin's version requires licensing (a mechanical - or compulsory - license and, for performance rights, a synchronization license).
Asking for permission from the copyright holder is a relatively painless process. Defending against a lawsuit is not.