By studying the existing higher order derivation formulas of rational B\'{e}zier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In this paper, we present a new derivation formula for rational B\'{e}zier curves that overcomes this drawback and show that the $k$th degree derivative of a $n$th degree rational B\'{e}zier curve can be written in terms of a $(2^kn)$th degree rational B\'{e}zier curve.we also consider the properties of the endpoints and the bounds of the derivatives.

翻译：通过研究现存的关于有理Bézier曲线的高阶求导公式，我们发现这些公式在求导阶数超过曲线次数时会失效。本文提出了一种克服该缺点的有理Bézier曲线新求导公式，并证明n次有理Bézier曲线的k阶导数可表示为(2^k n)次有理Bézier曲线。我们还讨论了导数端点性质及其界。