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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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Content

Derivatives of General Results
 
        Derivative of 
        General Polynomial Function

 
        Derivative of 
        General Trigonometric Function

 
        Derivative of 
        General Exponential and Logarithmic Function

 
        Derivative of 
        General Inverse Trigonometric Function

Derivatives of General Results

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

Derivative of General Polynomial Function

Derivative of General Linear Function

Proof by Epsilon-Delta definition:
Derivative of General Quadratic Function

Proof by Epsilon-Delta definition:
Derivative of General Power Function
Derivative of General Continued Product Function

Proof.

Or by Logarithmic Differentiation

Derivative of General Trigonometric Function

Derivative of General Sine Function
Derivative of General Cosine Function
Derivative of General Tangent Function
Derivative of General Cotagent Function
Derivative of General Secant Function
Derivative of General Cosecant Function

Derivative of General Exponential and Logarithmic Function

Derivative of General Natural Exponential Function
Derivative of General Exponential Function
Derivative of General Natural Logarithmic Function
Derivative of General Logarithmic Function

Derivative of General Inverse Trigonometric Function

Derivative of General Inverse Sine Function

General Inverse Sine Function

Proof

or
Derivative of General Inverse Cosine Function

General Inverse Cosine Function

Proof
Derivative of General Inverse Tangent Function

General Inverse Tangent Function

Proof
Derivative of General Inverse Cotangent Function

General Inverse Cotangent Function

or

Proof

or
Derivative of General Inverse Secant Function

General Inverse Secant Function

Proof
Derivative of General Inverse Cosecant Function

General Inverse Cosecant Function

Proof