Hyperbolic Functions

In this lesson, 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.

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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




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