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求z=xy/(x-y)的全微分,

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求z=xy/(x-y)的全微分,
我是怎么都做不出和答案一样的了.为什么呢,那位亲帮我做下详细过程吧,
求z=xy/(x-y)的全微分,
z=xy/(x-y)
dz=f'x(x,y)dx+f'y(x,y)dy
xy/(x-y)对x取偏导得
[y(x-y)-xy]/(x-y)²dx
xy/(x-y)对y取偏导得
[x(x-y)+xy]/(x-y)²dy
所以
dz=[y(x-y)-xy]/(x-y)²dx+[x(x-y)+xy]/(x-y)²dy
dz=-y²/(x-y)²dx+x²/(x-y)²dy