A simple identity for derivatives of the arctangent function

TL;DR

This paper introduces a new, simple identity for computing derivatives of the arctangent function, offering a faster, symbolic-free algorithmic approach as an alternative to existing formulas.

Contribution

The paper presents a novel, straightforward identity for arctangent derivatives that simplifies and accelerates computation without symbolic programming.

Findings

The new identity provides a computationally efficient method.

Algorithmic implementation significantly speeds up derivative calculations.

No symbolic programming required for derivatives of arctangent.

Abstract

We present an identity for the derivatives of the arctangent function as an alternative to the Adegoke - Layeni - Lampret formula. We show that algorithmic implementation of the proposed identity can significantly accelerate the computation since this approach requires no symbolic programming in determination of the derivatives for the arctangent function.