设函数z=f(x,y)(xy≠0)满足=y2(x2-1),则dz=______.

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问题 设函数z=f(x,y)(xy≠0)满足=y2(x2-1),则dz=______.

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答案(2x-y)dx-xdy

解析 设xy=u,=v,有x2=.则
f(u,v)=uv(-1)=u2-uv,即z=f(x,y)=x2-xy.
所以dz=(2x-y)dx-xdy.[img][/img]
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