From this page I know that a Bezier curve of degree $N$ has a derivative which is a Bezier curve of degree $N-1$, and I know how to calculate the control points of it: Derivatives of a Bezier Curve
However, how would i get the partial derivatives of X and Y to calculate a gradient, when I have a multivariate quadratic curve such as this:
$X = f(t) = 3.0*(1-t)^2+2.0*(1-t)t+4.0*t^2$
$Y = g(t) = 9.0*(1-t)^2+1.0*(1-t)t+3.0*t^2$
Where the above describe $(X,Y)$ points in a two dimensional space.