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Show That There Does Not Exist Any Function f(x,y)f ( x , y )

Question 159

Essay

Show that there does not exist any function f(x,y)f ( x , y ) with continuous second partial derivatives such that δfδx=2y\frac { \delta f } { \delta x } = 2 y and ∂f∂y=−2x\frac { \partial f } { \partial y } = - 2 x

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