A New Method for obtaining the nth Derivative of a Function of the Form y = l1(x)l2(x)l3(x)

Abstract

In this work, we use product rule and Leibnitz’s theorem to generate a new method which can be used to obtain the higher order derivatives of any functions which can be written as y = l₁(x)l₂(x)l₃(x). A Theorem that establishes the new method is presented proved by using mathematical induction. The new method does not require the knowledge of the preceding derivative before obtaining the succeeding ones.

Keywords: product rule, Leibnitz’s theorem, derivatives, numerical integrator, induction

Journal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 55 – 58