On differentiation with respect to filters

TL;DR

This paper introduces a new generalized concept of derivatives using filter theory, extending classical differentiation rules and demonstrating advantages over traditional derivatives.

Contribution

It presents a novel derivative concept based on filters, generalizing classical derivatives and establishing similar properties and rules.

Findings

New filter-based derivative concept generalizes classical derivatives

Properties and differentiation rules analogous to classical calculus are derived

Advantages of the new concept over traditional derivatives are demonstrated

Abstract

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really generalizes the previously known concept of the derivative. Properties and differentiation rules are obtained similar to the classical rules of differentiation of the derivative. The advantages of the new concept over the classical derivative are shown. Rules for calculating the derivative by a filter are obtained similar to the classical rules of differentiation.