若z = sin ( xy ) 则它的全微分dz =A：xcos (xy) B：(xdx+ydy) cos (xy) C：ycos (xy) D：(ydx+xdy) cos (xy)

分类: 作业答案 • 2022-07-08 08:36:08

问题描述：

若z = sin ( xy ) 则它的全微分dz =
A：xcos (xy)
B：(xdx+ydy) cos (xy)
C：ycos (xy)
D：(ydx+xdy) cos (xy)

答

dz=ycos(xy)dx+xcos(xy)dy

答

∂z/∂x=cos(xy)*y
∂z/∂y=cos(xy)*x
所以dz=ycos(xy)dx+xcos(xy)dy

答

dz=cos(xy)ydx+cos(xy)xdy=(ydx+xdy)cos(xy),选D

答

z=sin(xy)
dz = cos(xy) .[ xdy+ydz]
ans:b