为自己加油

求函数z=(x+y)/(x-y)的全微分．

因∂z/∂x=[(x-y)-(x+y)]/(x-y) ²=-2y/(x-y) ² ∂z/∂y=[(x-y)+(x+y)]/(x-y)²=2x/(x-y)² 且它们都是连续的，故由全微分公式得 dz=[-2y/(x-y)²]dx+[2x/(x-y)²]dy =[2/(x-y)²](xdy-ydx)