How to find d y d x by implicit differentiation given x y 3 = y + x ?

Question

How to find                     d        y                    d        x             by implicit differentiation given       x          y      3        =    y    +    x  ?

sayko11czj · Accepted Answer

On both sides, differentiate each term                     implicitly with respect to x                        Note differentiate               x          y      3                     using                             product rule                        (      x      .3              y        2            .                        d          y                          d          x                    +              y        3            .1      )        =                  d        y                    d        x              +    1        ⇒    3    x          y      2                      d        y                    d        x              -                  d        y                    d        x              =    1    -          y      3            ⇒                  d        y                    d        x                    (      3      x              y        2            -      1      )        =    1    -          y      3            ⇒                  d        y                    d        x              =                  1        -                  y          3                            3        x                  y          2                -        1

How to find d y d x by implicit differentiation given x y 3 =...

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