设z=f(x,y),)由方程z-y-x+xez-y-x=0确定,求dz.

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问题 设z=f(x,y),)由方程z-y-x+xez-y-x=0确定,求dz.

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答案对z-y-x+xez-y-x=0两边求微分,得dz-dy-dx+ez-y-xdx+xez-y-x(dz-dy-dx)=0,解得dz=[1+(x-1)ez-y-x]/(1+xez-y-x)dx+dy.

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