Calculus1 Lecture: 18 Higher Order Derivatives| Second, Third, and nth Derivatives скачать в хорошем качестве

Calculus1 Lecture: 18 Higher Order Derivatives| Second, Third, and nth Derivatives

In this lecture, we introduce higher-order derivatives and explain how successive derivatives of a function are defined and computed. Topics covered: Review of the first derivative using the limit definition Definition of higher-order derivatives Second and third derivatives Higher derivatives of polynomial functions A corollary for derivatives of polynomials Second derivative of rational functions A general formula for the nth derivative of 1/x ​ Several examples illustrate how repeated differentiation reveals patterns that lead to general formulas for higher-order derivatives. Instructor: Prof. Shadi Shaqaqha Department of Mathematics – Yarmouk University شرح المشتقات العليا (Higher-Order Derivatives) مثل المشتقة الثانية والثالثة والصيغة العامة للمشتقة رقم 𝑛 00:00 Definition of higher-order derivatives 01:41 Example 1 – Polynomial derivatives 02:56 Corollary for polynomials 03:35 Example 2 – Second derivative of a rational function 05:08 Example 3 – nth derivative of 1/x