Hyperbolic Function Derivatives

Abstract

Functions are defined as rules that relate each domain element to exactly one member of the codomain. The hyperbolic function is a combination of exponential functions that have inverses and derivatives and anti-derivatives of hyperbolic functions and their inverses (Faisal et al., 2012). The main hyperbolic functions are sinh x, cosh x, sech x, and csch x. The derivative of the hyperbolic function is calculated using the derivative of the exponential function formula and the identity formula of other hyperbolic functions. The derivative is a measure of how a function changes as its value changes or how one quantity changes when another quantity changes. Derivatives (derivatives) are the result of the process of differentiation or differentiation of a function. So, derivatives are closely related to differentials (Asyhar, 2018).