How to implicitly differentiate x y = x - 2 y ?

Question

How to implicitly differentiate                     x        y              =    x    -    2    y  ?

dalematealreypq3a · Accepted Answer

First, write it as                     (        x        y        )                              1          2                      =    x    -    2    y   or             x                        1          2                            y                        1          2                      =    x    -    2    y  .Next, differentiate both sides with respect to       x  , assuming that       y   is a function of       x  .  You&#039;ll need the Product Rule and the Chain Rule:                    1                    2                    x              -                  1          2                            y                        1          2                      +                  1                    2                    x                        1          2                            y              -                  1          2                      ⋅                  d        y                    d        x              =    1    -    2                  d        y                    d        x            .Finalize this equation to obtain                     d        y                    d        x            :                    d        y                    d        x                    (                        1                          2                            x                              1            2                                      y                  -                      1            2                              +      2      )        =    1    -                  1                    2                    x              -                  1          2                            y                        1          2                                        d        y                    d        x              =                  1        -                              1                                2                                    x                      -                          1              2                                                y                                    1              2                                                                        1                                2                                    x                                    1              2                                                y                      -                          1              2                                      +        2              =                  1        -                                                            y                                                          2                                          x                                                                                                                    x                                                          2                                          y                                                    +        2              =                  2                              x            y                          -        y                    x        +        4                              x            y

How to implicitly differentiate sqrt(xy)= x-2y?

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