Generalization and Cogitation of Leibniz Derivative Rule

Abstract

This study is about the generalization of Leibniz's derivative rule, which has been done as research. That is, obtaining an extension of the derivative of the nth order of the product of the nth function, which is the successive derivatives up to the nth order. Leibniz's rule is the derivative of the nth order of the product of two functions, which is in the form of an expansion and has successive derivatives up to the nth order. First, the generalization of a theorem in mathematics is explained. Also, the derivative of the product of two or more functions, then the derivatives of the first to the nth order of a function, and the rule of Leibniz's derivative are discussed and we have an overview of the generalization of this rule. The results show that the relationship between the order of rivatives of functions and coefficients in the general sentence of the generalized rule is the same as the relationship of owers and coefficients in the general sentence of the expansion of polynomials. To obtain the derivative of higher order in the multiplication of several functions, less process is easily used.