Obtaining Leibniz's rule for derivations in its most general form

TL;DR

This paper generalizes Leibniz's rule for various derivations using Newton's binomial formula, providing a concise method to compute the nth power of different derivations.

Contribution

It introduces a unified formula for Leibniz's rule applicable to generalized derivations, expanding the classical understanding.

Findings

Derived a short formula for nth power of derivations

Unified Leibniz's rule for different derivation types

Enhanced computational methods for derivations

Abstract

The main purpose of this paper is to obtain Leibniz's rule for generalized types of derivations via Newton's binomial formula. In fact, we provide a short formula to calculate the nth power of any kind of derivations.