You think that's magic? Wait till you learn about "automatic differentiation," in which you can mechanically and exactly take the derivative of a computer program (function) without a kludge like setting dx=0.001. In the "old days" this took the form of a transformation of the (say, Fortran) source code. In dynamic languages it can be almost trivial to implement.

The relevant wikipedia article is here, but it makes the process sound way more complicated than it really is: http://en.wikipedia.org/wiki/Automatic_differentiation

Here's a blog entry about it: http://nibot-lab.livejournal.com/65962.html?thread=108202