# Derivatives of Extended Regular Expressions

I'm trying to formulate the derivatives of a few extended regular expressions:

$$[c_1, c_2, . . . , c_n]$$ -- a range of characters
$$r^{n..}$$ -- r repeated n or more times (where n ≥ 0)
$$r^{n..m}$$ -- r repeated between n and m times (n ≥ 0, n and m inclusive)
$$r^+$$ -- r repeated one or more times

I want to do this without just converting them into basic regular expressions; e.g. for range, not just use alternation (+) on every character. To illustrate what I'm looking for, here's the derivative of another extended regular expression, r exactly n times:

$$der \:c (r^{n})= if n = 0, ∅; else \:if nullable(r),\: der\: c (r) • r^{(..n-1)};\: else \:der\: c (r) • r^{n-1}$$

• And what is your question? Also, you might want to come up with a title that's a little more specific than a book title. ;) – Raphael Oct 11 at 12:01