Hyperbolic Functions - Maple Programming Help

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Hyperbolic Functions

Main Concept

There are a total of six hyperbolic functions: sinhx, coshx, tanhx, cschx, sechx, cothx

Summary of the Hyperbolic Function Properties

 

Name        

Notation        

Equivalence

Derivative

Special properties

Hyperbolic Sine

sinh(x)

ex  ex2

ddxsinhx = coshx

sinh0 = 0 

Hyperbolic Cosine

cosh(x)

ex + ex2

ddxcoshx = sinhx

cosh0 = 1 

Hyperbolic Tangent

tanh(x)

sinhxcoshx= ex  exex + ex = e2x1e2x + 1

ddxtanhx = sech2x

tanh0 = 0 

Hyperbolic Cosecant

csch(x)

sinhx1 = 2ex  ex

ddxcschx = cothxcschx

Hyperbolic Secant

sech(x)

coshx1 = 2ex + ex

ddxsechx = sechxtanhx

sech0 = 1 

Hyperbolic Cotangent

coth(x)

coshxsinhx= ex + exex  ex = e2x+1e2x  1

ddxcothx = csch2x

cothx2cothx = cschx

 

Explore the properties of the Hyperbolic Functions.

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