Techniques of Differentiation

 

 

 

Contents

 

Differentiation

  

Sum & Difference Rules

  

Product Rule

  

Quotient Rule

  

Chain Rule

  

Exponential Function

  

Logarithmic Function

  

Trigonometric Function

  

Reciprocal Function

  

Inverse Function

2  

Implicit Differentiation

  

Higher Derivatives

  

Quiz

  

Calculus Main Page

Inverse Trigonometric Functions

 
 
Derivatives of the Inverse Functions
 
Inverse Sine Function:
             
             Let y = sin-1 x
             Then, x = sin y
 
           
 
           
 
the positive square root is taken as the range of values of y is from -p/2 to p/2 (principal values of the inverse function), for which cos y is positive.
 
Inverse Cosine Function:
 
             Let y = cos-1 x
             Then, x = cos y
 
                 
 
                
 
the positive square root is taken as the range of values of y is from 0 to p (principal values of the inverse function), for which sin y is positive.
 
Inverse Tangent Function:
 
             Let y = tan-1 x
             Then x = tan y
 
            
 
            
 
Examples on the next page.