 Bézier derivative control polygon

For a degree-$n$ Bézier curve, the $r$th derivative has degree at most $n-r$ and control points $n!{\Delta }^r{P}_j/(n-r)!$. The first derivative follows by differentiating the Bernstein basis and shifting one summation index; iteration proves the general formula. A parameter interval of length $h$ multiplies these derivative controls by $h^{-r}$.