设二元函数z=sin(x-y),求αz/αy,αy/αz,dz

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 16:30:23
设二元函数z=sin(x-y),求αz/αy,αy/αz,dz
x){nߓ]=O[}6uCmqfFnγM6VX@J'&Hd=v6٤lan`f]eT&5aEO0A+BCVJ%X I@)<;?l* *69B?@UD[rь=i)3NX~O]S^_l{fM [

设二元函数z=sin(x-y),求αz/αy,αy/αz,dz
设二元函数z=sin(x-y),求αz/αy,αy/αz,dz

设二元函数z=sin(x-y),求αz/αy,αy/αz,dz
∂z/∂x=cos(x-y)
∂z/∂y=-cos(x-y)
dz=∂z/∂x*dx+∂z/∂y*dy
=cos(x-y)dx-cos(x-y)dy

dz/dy=-cos(x-y)
dy/dz=-1/cos(x-y)
dz/dx=cos(x-y)
dz=cos(x-y)dx-cos(x-y)dy

题目有点错吧,应该是:
αz/αy=-cos(x-y)
αz/αx=cos(x-y)
dz=cos(x-y)dx-cos(x-y)dy