When should I use total differentials and when should I use implicit differentiation?An example of an equation where I'm unsure if to use total differentials or implicit differentiation is f ( x , y ) = x 2 yUsing total differentials ∂ f ∂ x d x + ∂ f ∂ x d y = 2 x y d x + x 2 d y, solving for d y d x = − 2 y x Using implicit differentiation: ( 2 x d y d x ) ( y ) + x 2 , solving for d y d x = − x y I'm unsure when to use each method and they both yield different results.

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When should I use total differentials and when should I use implicit differentiation?An example of an equation where I&#039;m unsure if to use total differentials or implicit differentiation is   f  (  x  ,  y  )  =      x    2    yUsing total differentials            ∂      f              ∂      x        d  x  +            ∂      f              ∂      x        d  y  =  2  x  y  d  x  +      x    2    d  y, solving for             d      y              d      x        =            −      2      y        x  Using implicit differentiation:  (  2  x            d      y              d      x        )  (  y  )  +      x    2  , solving for             d      y              d      x        =            −      x        y  I&#039;m unsure when to use each method and they both yield different results.

Mireya Hoffman · Accepted Answer

If       f                  x                  j                      =            ∂      f              ∂              x                  j                     then                    d        f                            =                              f                      x                          d        x        +                  f                      y                          d        y                                          =                    2        x        y        d        x        +                  x                      2                          d        y

When should I use total differentials and when should I use implicit differentiation? An example of an equation where I'm unsure if to use total differentials or implicit differentiation is f(x,y)=x^2y

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