Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151101On the $s^{th}$ derivative of a polynomial14114513010.22075/ijnaa.2015.130ENAbdullahMirDepartment of Mathematics, University of Kashmir, Srinagar, $190006$, (India)Journal Article20131024For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.https://ijnaa.semnan.ac.ir/article_130_55c76fca4b5e4d033c72d893fe0a47b7.pdf