There's a pretty variant of this idea introduced in 1995 by Valentin Antimirov called partial derivatives of regular expressions. His idea was to replace the single derivative with a set of partial derivatives that add up to the whole derivative. This simplifies the derivative algorithm quite a bit, and makes it possible to write amazingly concise and efficient regular expression matchers.
E.g., here's an implementation of a regular expression compiler that uses Antimirov derivatives to take a regexp and build a table-driven matcher in about 50 lines of code:
http://semantic-domain.blogspot.com/2013/11/antimirov-deriva...