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：通过研究现有的有理Bézier曲线高阶求导公式，我们发现当导数阶数超过曲线次数时，这些公式将失效。本文提出了一种新的有理Bézier曲线求导公式，该公式克服了这一缺陷，并证明了n次有理Bézier曲线的k阶导数可以表示为2^kn次有理Bézier曲线。我们还考虑了导数在端点处的性质及其界的问题。