Derivatives of General Results

Usually, general result of a function can be determined by the rule of composite function.

Derivative of General Polynomial Function

1. Derivative of General Linear Function

   

   Proof by Epsilon-Delta definition:

   

2. Derivative of General Quadratic Function

   

   Proof by Epsilon-Delta definition:

   

3. Derivative of General Power Function

   

4. Derivative of General Continued Product Function

   

   Proof.

   

   Or by Logarithmic Differentiation

   

Derivative of General Trigonometric Function

1. Derivative of General Sine Function

   

2. Derivative of General Cosine Function

   

3. Derivative of General Tangent Function

   

4. Derivative of General Cotagent Function

   

5. Derivative of General Secant Function

   

6. Derivative of General Cosecant Function

   

Derivative of General Exponential and Logarithmic Function

1. Derivative of General Natural Exponential Function

   

2. Derivative of General Exponential Function

   

3. Derivative of General Natural Logarithmic Function

   

4. Derivative of General Logarithmic Function

   

Derivative of General Inverse Trigonometric Function

1. Derivative of General Inverse Sine Function

   General Inverse Sine Function

   

   Proof

   

   or

   

2. Derivative of General Inverse Cosine Function

   General Inverse Cosine Function

   

   Proof

   

3. Derivative of General Inverse Tangent Function

   General Inverse Tangent Function

   

   Proof

   

4. Derivative of General Inverse Cotangent Function

   General Inverse Cotangent Function

   or

   Proof

   

   or

   

5. Derivative of General Inverse Secant Function

   General Inverse Secant Function

   

   Proof

   

6. Derivative of General Inverse Cosecant Function

   General Inverse Cosecant Function

   

   Proof