# Hyperbolic Functions

In these lessons, we will look at Hyperbolic Functions, Hyperbolic Identities, Derivatives of Hyperbolic Functions and Derivatives of Inverse Hyperbolic Functions and how to evaluate them. We will look at the graphs of some Hyperbolic Functions and the proofs of some of the Hyperbolic Identities.

Related Topics:

More Calculus Lessons

Calculus Games

## Definition of the Hyperbolic Function

## Hyperbolic Identities

## Derivatives of Hyperbolic Functions

**Example:**

Differentiate

**Solution:**

Using the table above and the Chain Rule.

## Derivatives of Inverse Hyperbolic Functions

Example:

Find the derivative of

**Solution:**

Using the above table and the Chain Rule

## Videos - Hyperbolic Functions and their Derivatives

Hyperbolic Functions - The Basics

This video gives the definitions of the hyperbolic functions, a rough graph of three of the hyperbolic functions, evaluate a few of the functions at different values, and justify a couple of identities.

Introduction to Hyperbolic Functions

This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.

Hyperbolic Functions - Derivatives

This video shows the formulas for the derivatives of the hyperbolic functions and finds a few derivatives.

Inverse Hyperbolic Functions - Derivatives

This video gives the formulas for the derivatives on the inverse hyperbolic functions and does 3 examples of finding derivatives.

## Proof of Hyperbolic Identities

Prove a Property of Hyperbolic Functions: (sinh(x))

^{2} - (cosh(x))

^{2} = 1

This video shows a proof of one of the properties of hyperbolic functions.

Prove a Property of Hyperbolic Functions: (tanh(x))^2 + (sech(x))^2 = 1

Prove a Property of Hyperbolic Functions: sinh(x+y)=sinh(x)cosh(y)+cosh(x)sinh(y)

Prove a Property of Hyperbolic Functions: (sinh(x))^2=(-1+cosh(2x))/2

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.