求函数的全微分：z=xe-xyy+sin(xy)

求函数的全微分：
z=xe-xyy+sin(xy)
【正确答案】：dz=e-xydx+xe-xy(-ydx-xdy)+cos(xy)(ydx+xdy) =[e-xyxye-xy+ycos(xy)]dx+[-x2e-xy+xcos(xy)]dy．