lnz=xyln(x+y)
两边对x求导得
z'x/z=yln(x+y)+xy/(x+y)
z'x=z[yln(x+y)+xy/(x+y)]
两边对y求导得
z'y/z=xln(x+y)+xy/(x+y)
z'x=z[xln(x+y)+xy/(x+y)]
dz=z'xdx+z'ydy
=z[yln(x+y)+xy/(x+y)]dx+z[xln(x+y)+xy/(x+y)]dy