Summary of Calculus of the Hyperbolic Functions

Hyperbolic functions are defined in terms of exponential functions.
Term-by-term differentiation yields differentiation formulas for the hyperbolic functions. These differentiation formulas give rise, in turn, to integration formulas.
With appropriate range restrictions, the hyperbolic functions all have inverses.
Implicit differentiation yields differentiation formulas for the inverse hyperbolic functions, which in turn give rise to integration formulas.
The most common physical applications of hyperbolic functions are calculations involving catenaries.

Glossary

catenary: a curve in the shape of the function [latex]y=a\text{cosh}(x\text{/}a)[/latex] is a catenary; a cable of uniform density suspended between two supports assumes the shape of a catenary