设z=f(x,y)由方程z+x+y=e^(z+x+y)所确定,求Dz
问题描述：
设z=f(x,y)由方程z+x+y=e^(z+x+y)所确定,求Dz
答
方程两边对x求导：z'x+1=e^(z+x+y)*(z'x+1),解得：z'x=-1
方程两边对y求导：z'y+1=e^(z+x+y)*(z'y+1),解得：z'y=-1
所以dz=z'xdx+z'ydy=-dx-dy