求教几个高等数学题1.求f(x,y)=xsin(x+y)+ycos(x+y)的二级偏导数2.求Z=xsin(x2+y2)

1 Z=xsin(x+y)+ycos(x+y)
Zx=sin(x+y)+xcos(x+y)-ysin(x+y)
Zy=xcos(x+y)+cos(x+y)-ysin(x+y)
所以Zxx=cos(x+y)+cos(x+y)-xsin(x+y)-ycos(x+y)=
2cos(x+y)-xsin(x+y)-ycos(x+y)
Zxy=Zyx=cos(x+y)-xsin(x+y)-sin(x+y)-ycos(x+y)
Zyy=-xsin(x+y)-sin(x+y)-sin(x+y)-ycos(x+y)=
-2sin(x+y)-xsin(x+y)-ycos(x+y)
2 Z=xsin(x2+y2)
Zx=sin(x2+y2)+2x2cos(x2+y2)
Zy=2xycos(x2+y2)
所以全微分=[sin(x2+y2)+2x2cos(x2+y2)]dz+[2xycos(x2+y2)]dy
3 Z=2x+3y2
Zx=2
Zy=6y
△z=Z(12,8.3)-Z(10,8)=230.67-212=18.67
dz=2dx+6ydy=2*2+6*8*0.2=13.6