Comment on "note on the derivative of the hyperbolic cotangent"

TL;DR

This paper refutes previous claims that the derivative of hyperbolic cotangent includes an additional delta function term, reaffirming the standard derivative expression.

Contribution

It provides a rigorous argument demonstrating that the standard derivative of hyperbolic cotangent is complete without additional delta function terms.

Findings

Standard derivative of coth y is correct as -csch^2 y

Previous claims of an extra delta function term are incorrect

Reaffirms established mathematical results

Abstract

In a couple of articles (Ford G W and O'Connell R F 1996 Nature 380 113 and 2002 J. Phys. A: Math. Gen. 35 4183) it was argued that the standard result for the derivative of the hyperbolic cotangent in the literature, d \coth y/dy = -{csch}^2 y is incomplete and the correct expression should have an additional term proportional to the Dirac delta function. The purpose of this paper is to demonstrate that this claim is incorrect.