Functions and Analysis

On the Conceptual Limitations of the Theoretical Substantiation of the Derivatives of Inverse Trigonometric and Hyperbolic Functions

Authors: Vitaliy Boltian

This paper addresses the conceptual limitations in classical mathematical analysis regarding the differentiation of inverse trigonometric and hyperbolic functions. The traditional approach, which relies heavily on the inverse function theorem and complex virtual transformations, is reconsidered. The author introduces a novel theoretical framework based on a system of real companion functions and defines the concept of a "transition coefficient". This approach establishes direct, invariant relations between trigonometric, hyperbolic, and algebraic function systems within the real domain. The practical application of the proposed apparatus is demonstrated through specific integration examples, showcasing a significant simplification of mathematical operations and analytical structures.

Comments: 3 Pages.

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Submission history

[v1] 2026-09-23 11:45:16

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