Bezier curve derivative problem

Hi,

I'm new to this forum. I have a bezier curve that I'm using in a programming context, which I'd like to get the derivative of: basically, it's being used a curve by which to interpolate distance/time (speed), and what I'd like to get is a graphic representation of speed/time (acceleration).

I've followed several tutorials elsewhere on the internet but the results I get don't make sense. The function for the curve is

x(t) = (6p-2)t^3+(3-9p)t^2+3pt

y(t) = -2t^3+3t^2

the added variable p is an "influence" value that affect the curvature, and ranges only from 0<p<1. Also, the range of t I am interested in is 0<t<1. Depending on the value of p this curve can either be straight, or a fairly exaggerated "s" shape, going from [0,0] to [1,1].

The derivative curve *should* look like an arc, beginning at [0,0], arcing upwards, changing direction at x=0.5 and arcing back down to [1,0]. I just can't figure out how to write the function.

Really hoping someone can help!