Basic Rules of Differentiation

Derivatives of a Few Simple Functions

Rules Of Differentiation

1. Constant-Function Rule:

The derivative of a constant function  or  is identically zero i.e., zero for all values of 

Given a function 

The derivative is 

Exercise:

(i) If  

Solution 

(ii)  If 

Solution

2. Power - Function Rule :

The derivative ofd a power function  is 

Symbolically,

For the special case of n = 1, the derivative of  is the constant 1

 

Therefore,

                  

Exercise

(i) If 

     Solution:

     

     

(ii) If 

      Solution:

      

(iii) If 

      Solution:

      

(iv) If 

      Solution:

      

(v) If  

      Solution:

      

(vi) If 

      Solution:

      

 (vii) If 

      Solution: 

       

3.  (Constant Function Rule Generalised)

      Constant times a Function Rule:

      When a multiplicative constant appears in the function, so that , its derivatives is the           constant times the derivatives of the functions.

        or 

      Excercise:

      (i) If 

      Solution:

      

     (ii) If 

      Solution:

       

      (iii) If 

      Solution:

       

(iv) If 

      Solution:

      

4.  Square-root Rule: 

     The derivative of a function involving square-root   is  

     Symbolically,

       or 

     Excercise:

(i) If 

    Solution:

    

(ii) If 

    Solution:

    

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