设二元函数z=sin(x-y),求αz/αy,αy/αz,dz

题目

设二元函数z=sin(x-y),求αz/αy,αy/αz,dz

答案

∂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