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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

1. 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:

2. 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:

3. 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:

4. 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:

5. 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:

6. 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:

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

References

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

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