Techniques of Differentiation

 

 

 

Contents

 

Differentiation

  

Sum & Difference Rules

  

Product Rule

  

Quotient Rule

  

Chain Rule

  

Exponential Function

  

Logarithmic Function

  

Trigonometric Function

  

Reciprocal Function

  

Inverse Function

  

Implicit Differentiation

  

Higher Derivatives

  

Quiz

  

Calculus Main Page

Quotient Rule

 
 
The quotient rule is used to differentiate expressions that are quotients of two functions.
 
Given
              , then
          
 
 
Differentiate the following w.r.t x:
     (i)  
     (ii) 
     (iii)
     (iv)
     (x) 
 
Solution:
 
(i) 
       
 
(ii)
      
 
(iii)
      
 
(iv) This question can be solved in 2 ways.
 
Method 1: Differentiate directly from the expression.
      
 
Method 2 : Use the idea of partial fractions.
      
Using cover-up rule,
      
      
 
The answers that both methods yield are the same, only expressed differently.
 
(v)