What constitutes a "derivative work?"

According to U.S. copyright law, a derivative work is one that contains "recast, transformed, or adapted" materials from another work. Here is the relevant definition, from U.S. Code, Title 17, Paragraph 101:

A “derivative work” is a work based upon one or more preexisting works, such as a translation, musical arrangement, dramatization, fictionalization, motion picture version, sound recording, art reproduction, abridgment, condensation, or any other form in which a work may be recast, transformed, or adapted. A work consisting of editorial revisions, annotations, elaborations, or other modifications which, as a whole, represent an original work of authorship, is a “derivative work”.

In theory, "transformed" covers remixing, sampling, etc. These uses, therefore, would also be considered "derivative use."

One thing that is not mentioned is "transcoding," i.e. converting from FLAC to MP3, JPEG to TIFF, etc. This is such a trivial "transformation" that it shouldn't be considered a derivative work, but an actual copy of the work. This also applies to e.g. printing out a web page, or recording digital music onto a cassette tape. Such copying is only allowed under the terms of the license.

However, you should keep in mind that many derivative works (and other uses) fall under fair use. Fair use trumps all copyright licenses, including this one. If your use is truly fair use, then you don't need to ask permission.

The line between "transformed derivative use" and "fair use" can often be hard to distinguish, even among legal professionals. In general, if the "new" work is does not supercede the original, is not done for profit, does not contain substantial portions of the original, and does not affect the original work's value in the marketplace, then it's probably fair use.

But it's a huge grey area, and sometimes things that really should be considered fair use are found to be infringing. From your perspective, the safest thing to do is to abide by the license, or contact me for authorization.