【正确答案】正确答案：因z=e ^xy sin(x+y)，于是 dz=d[e ^xy sin(x+y)]=d(e ^xy ).sin(x+y)+ee ^xy d[sin(x+y)] =e ^xy .(ydx+xdy).sin(x+y)+e ^xy .cos(x+y)(dx+dy) =e ^xy ｛[ysin(x+y)+cos(x+y)]dx+[xsin(x+y)+cos(x+y)]dy｝