Differentiation Skill Example

Lets assume that the student asked what the solution to the below questions.

 

Differentiate the functions given below.

1.                2.                3.

 

You can solve this question by seeing the solutions to the given questions below, which use the same concepts as the student’s questions.

 

 

Questions which will help you to solve your question.

 

Question 1: Differentiate

 

Answer:  and           (Quotient rule)

Where                     and                  

Let                                                  

Then                                                    

                                      

                                       

                                                       (Chain rule)

                                   

                                       

 

Substituting, u(x), v(x),  and in  gives:

 

 

Determine u and v in your question, find  and , then follow the above steps in the use of chain and quotient rules.

 

Question 2: Differentiate

 

Answer:      then                 (Product Rule)

Let                              and                 

Let                                                               

Then                                                         

                                                  

                                                               

                                          (Chain Rule)

Hence,                    and                 

Substituting u, v,  and  in  gives

 

 

Determine u and v in your question, find  and , then follow the above steps in the use of chain and product rules.

 

Question 3: Differentiate

 

Answer:

Let                      then            

And                        where         and                  and

 

                (Quotient Rule)

 

Note that         and      

Then                            and                      (Product Rule)

Substituting u, v,  and  in  gives

 

Now              (Chain Rule)

        and