高数 求偏导数已知sinxy-2z+e^z=0,求偏z/偏x和偏z/偏y

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d(sinxy-2z+e^z)=0
dsinxy-d2z+de^z=0
ycosxydx+xcosxydy-2dz+e^zdz=0
ycosxydx+xcosxydy=2dz-e^zdz=(2-e^z)dz
dz=ycosxy/(2-e^z)dx+xcosxy/(2-e^z)dy
所以偏z/偏x=ycosxy/(2-e^z)
偏z/偏y=xcosxy/(2-e^z)
======以下答案可供参考======
供参考答案1:
对x求导：ycosxy-2z'x+z'xe^z=0,得：z'x=ycosxy/(2-e^z)
对y求导：xcosxy-2z'y+z'ye^z=0,得: z'y=xcosxy/(2-e^z)