两边求z的x偏导数得z'(x)+z'(x)e^z=y+2x, 所以z'(x)=(y+2x)/(1+e^z).两边求z的y偏导数得z'(y)+z'(y)e^z=x+3y^2, 所以z'(y)=(x+3y^)/(1+e^z).所以dz=z'(x)dx+z'(y)dy=[(y+2x)dx+(x+3y^)dy]/(1+e^z).
