How exactly is this happening?I was studying Derivative and my book says if: y = ( 1 + x 2 ) 3 Then its derivative is: y ′ = 3 ( 2 x ) ( 1 + x 2 ) 2 2 ( 1 + x 2 ) − 1 = 3 x ( 1 + x 2 ) I can't understand how the writer has changed the first derivative fraction into the second one. In other words, how did he simplify?Note: I'm really really basic, so please explain in details.Thank you.

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How exactly is this happening?I was studying Derivative and my book says if:  y  =      (    1    +          x      2              )      3      Then its derivative is:      y    ′    =            3      (      2      x      )      (      1      +              x        2                    )        2                    2              (        1        +                  x          2                          )                      −            1                                =  3  x      (    1    +          x      2        )  I can&#039;t understand how the writer has changed the first derivative fraction into the second one. In other words, how did he simplify?Note: I&#039;m really really basic, so please explain in details.Thank you.

humusen6p · Accepted Answer

Observe that      (    1    +          x      2              )      3        =  (  1  +      x    2        )          3              /            2      Thus                                          (            (            1            +                          x              2                                      )                              3                                  /                                2                                      )                    ′                                    =                  3          2                (        1        +                  x          2                          )                      3                          /                        2            −            1                          (        1        +                  x          2                          )          ′                                                  =                  3          2                (        1        +                  x          2                          )                      1                          /                        2                          2        x        =                  3                                                    ⧸                                      2                          (        1        +                  x          2                          )                      1                          /                        2                                                ⧸                          2        x                                          =        3        x                  1          +                      x            2                              The first equation is due to the chain rule. i.e.            (      f              (        g        (        x        )        )            )        ′    =      f    ′    (  g  (  x  )  )      g    ′    (  x  )with   f  (  x  )  =      x          3              /            2       and   g  (  x  )  =  (  1  +      x    2    )

How exactly is this happening? I was studying Derivative and my book says if: y = <msqrt

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