对x求偏导：2yz+2xyZ'x=2x+2zZ'x,得Z'x=(x-yz)/(xy-z)
对y求偏导：2xz+2xyZ'y=2y+2zZ'y,得Z'y=(y-xz)/(xy-z)
所以dz=Z'xdx+Z'ydy=[(x-yz)dx+(y-xz)dy]/(xy-z)