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A Differential Operator Needed in the generation of a numerical Integrator for Environmental Models

Mercy Nduku Ngungu


In this research we generate a series method for computing the nth order derivative of a function that depends on five Independent variables by using the Leibnitz’s theorem in the product rule. Further, the theorem that establishes the new method and its proof are presented by using Mathematical Induction. It is established that the new series method does not require the knowledge of the preceding derivative before obtaining the succeeding ones.


Product rule, Leibnitz’s Theorem, Higher Order Derivatives, Mathematical Induction


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