设函数f(x,y)=(x-y)/(x+y),求函数f(x,y)在x=0,y=2的全微分

题目

设函数f(x,y)=(x-y)/(x+y),求函数f(x,y)在x=0,y=2的全微分

答案

df(0,2)=f'x(0,2)dx+f'y(0,2)dy
f'x(x,y)=2y/(x+y)^2,f'y(x,y)=-2x/(x+y)^2
代入即可.