### Essential Concepts

- 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