hmm, it's not obvious (to me!) in the single-line case, but that might be because of the high-frequency noise that makes the derivative sort of random.
I suppose one can incorporate uncertainty on f(t) by having g(y,t) = gausy(0,\sigma(t)) * \delta(y-f(t)) (which would also effectively antialias in the few-lines case).
Also I guess you have to be careful not to plot a Weierstrass Function!