设函数Y=f（x）由方程xy+y^2-2x=0,则dy/dx=?

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设函数Y=f（x）由方程xy+y^2-2x=0,则dy/dx=?
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设函数Y=f（x）由方程xy+y^2-2x=0,则dy/dx=?
设函数Y=f（x）由方程xy+y^2-2x=0,则dy/dx=?

设函数Y=f（x）由方程xy+y^2-2x=0,则dy/dx=?
xy+y^2-2x=0
y+xy'+2yy'-2=0
(x+2y)y'=2-y
y'=(2-y)/(x+2y)
dy/dx=(2-y)/(x+2y)