设z=z(x,Y)由xyz=x+y+z确定,求

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问题 设z=z(x,Y)由xyz=x+y+z确定,求

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答案xyz=x+y+z两边对x求偏导得yz+xydz/dx=1+dz/dx,解得dz/dx=(1-yz)/(xy-1),故d2z/dx2=[-ydz/dx(xy-1)-y(1-yz)]/(xy-1)2=2y(yz-1)/(xy-1)2

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