Derivatives of Hyperbolic Functions

In many physical problem, there usually exists the combination of the terms ex and e-x. Hyperbolic functions are analogs of the trigonometric function with the imaginary i of the complex exponentials are removed.

Hyperbolic Functions

The hyperbolic functions are defined as following:

• Hyperbolic Sine Function

  

• Hyperbolic Cosine Function

  

• Hyperbolic Tangent Function

  

• Hyperbolic Cotangent Function

  

• Hyperbolic Secant Function

  

• Hyperbolic Cosecant Function

  

Derivatives of Hyperbolic Functions

1. Derivative of Hyperbolic Sine Function

   

   Proof:

   

2. Derivative of Hyperbolic Cosine Function

   

   Proof:

   

    

3. Derivative of Hyperbolic Tangent Function

   

   Proof:

   

    

4. Derivative of Hyperbolic Cotangent Function

   

   Proof:

   

    

5. Derivative of Hyperbolic Secant Function

   

   Proof:

   

6. Derivative of Hyperbolic Cosecant Function

   

   Proof: