It might no longer be relevant but in
Generalized Functions, Volume 1: Properties and Operations, by I.M.Gel'fand and G.E.Shilov, Academic Press: 1964, pp 184-185, the formula V p 185 gives the kth derivative of delta(f(x)).
Written in a simplified LaTeX style it is:
(d^k/dx^k) delta(f(x)) = sum_n frac{ 1}{|f'(x_n)|} (frac{1}{f'(x)} d/dx)^k delta(x-x_n)
where f(x) is an infinitely differentiable function of x with any number n of simple roots.
For instance delta(sin x) = sum_n delta(x-n pi).
A well known formula in radio-astronomy (see Ron Bracewell's book),known as the "picket fence" function. (Here in the Australian outbackwhere our radio-telescopes are sited, fences indeed extend indefinitelyin straight lines!)
Gel'fand & Shilov's proofs are "elementary" and so is most of this volume even though it reaches higher than far more advanced text books. Itdoes not require "non-standard" analysis...
Unfortunately it is out of print!
Rene' Grognard.
> Date: Sun, 07 Jul 2013 19:46:26 -0400
> From: "Richard Hennessy" <rich.hennessy at verizon.net>
> Cc: Maxima List <maxima at math.utexas.edu>
> Subject: Re: [Maxima] pw.mac problem