Sideway
output.to from Sideway
Draft for Information Only

Content

Derivatives of Inverse Hyperbolic Functions
  Derivatives of Inverse Hyperbolic Functions

Derivatives of Inverse Hyperbolic Functions

Inverse trigonometric functions are often found in physical applications.

Derivatives of Inverse Hyperbolic Functions

  1. Derivative of Inverse Hyperbolic Sine Function

     IMAGE...

    y is the value lying between -∞ and ∞ and x is the value of sinh y from -∞ to ∞. The slope of the curve is always positive, imply dy/dx is always positive.

     IMAGE...

    Proof:

     IMAGE...
  2. Derivative of Inverse Hyperbolic Cosine Function

     IMAGE...

    y is the value lying between 0 and ∞  or between 0 and -∞ and x is the value of sinh y from 1 to ∞. The slope of the curve is either always positive or always negative, imply dy/dx is either always positive or always negative.

     IMAGE... or  IMAGE...

    Proof:

     IMAGE...
  3. Derivative of Inverse Hyperbolic Tangent Function

     IMAGE...

    y is the value lying between -∞ and ∞ and x is the value of sinh y from -1 to 1. The slope of the curve is always positive, imply dy/dx is always positive.

     IMAGE...

    Proof:

     IMAGE...

     

  4. Derivative of Inverse Hyperbolic Cotangent Function

     IMAGE...

    y is the value lying between -∞ and ∞ and x is the value of sinh y from -1 to ∞ and 1 to ∞. The slope of the curve is always negative, imply dy/dx is always negative.

     IMAGE...

    Proof:

     IMAGE...
  5. Derivative of Inverse Hyperbolic Secant Function

     IMAGE...

    y is the value lying between 0 and ∞  or between 0 and -∞ and x is the value of sinh y from 0 to 1. The slope of the curve is either always positive or always negative, imply dy/dx is either always positive or always negative.

     IMAGE...   or  IMAGE...

    Proof:

     IMAGE...
  6. Derivative of Inverse Hyperbolic Cosecant Function

     IMAGE...

    y is the value lying between -∞ and ∞ and x is the value of sinh y from -∞ to -1  and 1 to ∞. The slope of the curve is always negative, imply dy/dx is always negative.

     IMAGE...

    Proof:

     IMAGE...

©sideway

ID: 130700018 Last Updated: 9/7/2013 Revision: 0 Ref:

close

References

  1. S. James, 1999
  2. B. Joseph, 1978
close

Latest Updated LinksValid XHTML 1.0 Transitional Valid CSS!Nu Html Checker Firefox53 Chromena IExplorerna
IMAGE

Home 5

Business

Management

HBR 3

Information

Recreation

Hobbies 7

Culture

Chinese 1097

English 337

Reference 67

Computer

Hardware 149

Software

Application 187

Digitization 24

Numeric 19

Programming

Web 757

CSS 1

ASP.NET 1

Regular Expression 1

HTML

Knowledge Base

Common Color 1

Html Entity (Unicode) 1

Html 401 Special 1

OS 389

MS Windows

Windows10 1

.NET Framework 1

DeskTop 7

Knowledge

Mathematics

Formulas 8

Algebra 20

Number Theory 206

Trigonometry 18

Geometry 18

Calculus 67

Complex Analysis 21

Engineering

Tables 8

Mechanical

Mechanics 1

Rigid Bodies

Statics 92

Dynamics 37

Fluid 5

Fluid Kinematics 5

Control

Process Control 1

Acoustics 19

FiniteElement 2

Physics

Electric 10

Biology 1

Geography 1


Copyright © 2000-2019 Sideway . All rights reserved Disclaimers last modified on 06 September 2019