Derivative of f ( x ) = x 2 − 1 x I have the function following: f ( x ) = x 2 − 1 x And here is what I did: f ( x ) = x 2 − 1 x = ( x 2 − 1 ) 1 2 x f ′ ( x ) = x ⋅ 1 2 ( x 2 − 1 ) − 1 2 ( 2 x ) − ( x 2 − 1 ) 1 2 x 2 = x 2 ( x 2 − 1 ) − 1 2 − ( x 2 − 1 ) 1 2 x 2 And I'm pretty sure that this is wrong, and the answer book says it isn't either.I think I messed up somewhere, or didn't do it properly.I tried using the quotient rule. Do I need to make it into an exponent, and solve it as a chainrule?Please help me find the steps and answer to this question. Thank you.Or is there any other steps so it can match this?: 1 x 2 x 2 − 1

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Derivative of   f  (  x  )  =                              x          2                −        1            x      I have the function following:  f  (  x  )  =                              x          2                −        1            x      And here is what I did:  f  (  x  )  =                              x          2                −        1            x        =                    (                  x          2                −        1                  )                                    1              2                                          x            f    ′    (  x  )  =                    x        ⋅                              1            2                          (                  x          2                −        1                  )                      −                                          1                2                                                    (        2        x        )        −        (                  x          2                −        1                  )                                    1              2                                                  x        2              =                    x        2            (              x        2            −      1              )                  −                                    1              2                                          −      (              x        2            −      1              )                              1            2                                      x      2      And I&#039;m pretty sure that this is wrong, and the answer book says it isn&#039;t either.I think I messed up somewhere, or didn&#039;t do it properly.I tried using the quotient rule. Do I need to make it into an exponent, and solve it as a chainrule?Please help me find the steps and answer to this question. Thank you.Or is there any other steps so it can match this?:      1                  x        2                              x          2                −        1

Mateo Barajas · Accepted Answer

f  (  x  )  =                    x        2            −      1        x    f  (  x  )  =      u    v  Note that   u  =            x      2        −    1  ,   v  =  x and       v    ′    =  1 We then note that       u    ′    =      x                  x        2            −      1            f    ′    (  x  )  =                    u        ′            v      −      u              v        ′                    v      2        =                              x          2                                      x            2                    −          1                    −                        x          2                −        1                    x      2        =                              x          2                                      x            2                    −          1                    +                        −          (                      x            2                    −          1          )                                      x            2                    −          1                            x      2        =                              x          2                −                  x          2                −        1                              x          2                1                    x      2        =      1                  x        2                              x          2                −        1

pokoljitef2 · Accepted Answer

All your steps are fine, but your final answer can be simplified further to match the answer in your book.                                                        x              2                        (                          x              2                        −            1                          )                              −                1                                  /                                2                                      −            (                          x              2                        −            1                          )              2                                            x            2                                              =                                                            x                2                                                              x                  2                                −                1                                      −                                          x                2                            −              1                                            x            2                                                            =                                                            x                2                                                              x                  2                                −                1                                      −                                                            x                  2                                −                1                                                              x                  2                                −                1                                                          x            2                                                            =                              1                                          x                2                            −              1                                            x            2                                                            =                  1                                    x              2                                                                        x                  2                                −                1

Derivative of f ( x ) = <mrow class="MJX-TeXAtom-ORD"> <msqrt>

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