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 studentâ€™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