::Hi Doctormatt, perhaps we could say that a "derivative is the rate of change of a function or quantity at a certain time."  That seems fairly unequivocal and much more accessible than what is currently there.  I'm not so much a proponent of my own version so much as an *opponent* of the use of the meaningless (to the non-mathematical) word "instantaneous."

I don't really mind the differentiation thing being right after the initial sentence, because people might have clicked on the derivative page after going to differentiation (a disambig page).  It's certainly grammatical to say "Finding a derivative is called differentiation"; see gerund.  However, now that I think about it, maybe we should just say "Differentiation is the process of finding a derivative."  (We put the sentence in the active voice.)

Your thoughts?

Best,