On the bounds of the derivative of rational Bézier curves

According to some identities and inequalities about the intermediate weights and control points of the de Casteljau algorithm for rational Bézier curve, we derive a new bound of the derivative of rational Bézier curves. The comparison of the new bounds with some existing ones is also presented. Based on some previous bounds, the bound presented in this paper and many numerical examples, we propose a conjecture of the bound for the derivative of rational Bézier curves.