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~~Calculus~~

Calculus TOC Calculus~~Differentiation~~Integration

Differentiation, Derivative~~Rules of Differentiation~~Applications of Differentiation

Polynomial Trigonometric Exp() and Log()Inv Trigonometric Hyperbolic~~Inv Hyperbolic~~Implicit Equation General Result Successive Differentiation Parametric Equation Polar Equation Summary

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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

Derivative of Inverse Hyperbolic Sine Function

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.

Proof:
Derivative of Inverse Hyperbolic Cosine Function

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.

or

Proof:
Derivative of Inverse Hyperbolic Tangent Function

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.

Proof:
Derivative of Inverse Hyperbolic Cotangent Function

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.

Proof:
Derivative of Inverse Hyperbolic Secant Function

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.

or

Proof:
Derivative of Inverse Hyperbolic Cosecant Function

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.

Proof: