I need to find the derivatives of ( 1 + x y ) 3 = y x − 1 I tried this and stuck 3 ( 1 + x y ) 2 ( 0 + x ( d y d x ) + y ) = − y x − 2 + ( x − 1 d y d x ) d y d x ( x + y − x − 1 ) = − y x − 2 − 3 ( 1 + x y ) 2 d y d x = − y x 2 − 3 ( 1 + x y ) 2 x + y − x − 1 I'm not quite sure how to simplify it to achieve the final answer - − y ( 3 x 2 ( 1 + x y ) 2 + 1 x ( 3 x 2 ( 1 + x y ) 2 − 1

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I need to find the derivatives of  (  1  +  x  y      )    3    =  y      x          −      1      I tried this and stuck  3  (  1  +  x  y      )    2    (  0  +  x  (            d      y              d      x        )  +  y  )  =  −  y      x          −      2        +  (      x          −      1                  d      y              d      x        )            d      y              d      x        (  x  +  y  −      x          −      1        )  =  −  y      x          −      2        −  3  (  1  +  x  y      )    2              d      y              d      x        =            −      y              x        2            −      3      (      1      +      x      y              )        2                    x      +      y      −              x                  −          1                    I&#039;m not quite sure how to simplify it to achieve the final answer -            −      y      (      3              x        2            (      1      +      x      y              )        2            +      1              x      (      3              x        2            (      1      +      x      y              )        2            −      1

Envetenib8ne · Accepted Answer

Applying the d operator to both sides as I think you have done we have  3  (  1  +  x  y      )    2    (  y  +  x      y    ′    )  =      y    ′        1    x    −      y          x      2          ⟹    3  y  (  1  +  x  y      )    2    +  3  x  (  1  +  x  y      )    2        y    ′    =      y    ′        1    x    −      y          x      2      which we can solve for       y    ′   as follows      y    ′    (      1    x    −  3  x  (  1  +  x  y      )    2    )  =  3  y  (  1  +  x  y      )    2    +      y          x      2            ⟹        y    ′    =            3      y      (      1      +      x      y              )        2            +              y                  x          2                                    1        x            −      3      x      (      1      +      x      y              )        2              =            3              x        2            y      (      1      +      x      y              )        2            +      y              x      −      3              x        3            (      1      +      x      y              )        2

I need to find the derivatives of (1+xy)^3=yx^(−1) using the Implicit differentiation

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