Question

已知函数 z=ycos(x-2y) ,求 dz=

Answer 1

dz=(∂z/∂x)dx+(∂z/∂y)dy，其中

∂z/∂x=-ysin(x-2y)
∂z/∂y=cos(x-2y)+2ysin(x-2y)
所以dz=-ysin(x-2y)dx+[cos(x-2y)+2ysin(x-2y)]dy

Answer 2

因为z=ycos(x-2y),则计算全微分有：
dz=cos(x-2y)dy-ysin(x-2y)(dx-2dy).
=[2ysin(x-2y)+cos(x-2y)]dy-ysin(x-2y)dx