Example:
            Find the derivative ofwith respect to x.
Solution:
                        We have
            
            Diff: w.r.t 'x'
       
             
             
          
               

                

Example:
            Findif
Solution:
                        We have
            
            Diff: w.r.t 'x'
       
             
             
              
              

               

Example:
            Differentiatewith respect to 'x'.
Solution:
                        We have
                        

            Diff: w.r.t 'x'
             
             
             
             
              
              

               

Example:
            Differentiate with respect to 'x'.
Solution:
                        We have
            
            Diff: w.r.t 'x'.
       
              
              

               

Example:
            Find if
Solution:
                        We have
            
            Diff: w.r.t 'x'
       
                            By Quotient Rule
       
             
             
              
              
              
              
               

                

Example:
            Differentiate with respect to
Solution:
                        We have
            
Let
I.                              we have
            
            Diff: w.r.t. 'x'
            
In the previous example, we calculated
            
II.            We have
            
            Diff: w.r.t 'x'
                   
              
             
              
III.           By Chain Rule.
            
                   

              

(General Theorems of Differentiation)

Differential Calculus

(Differentiation of Trigonometric Functions)