Question

急求设f(x+y.x-y)=xy+y2求df(x.y).注：y2是y的平方.

Answer 1

设u=x+y,v=x-y

解得x=(u+v)/2,y=(u-v)/2

则f(x+y,x-y)=xy+y2可变为

f(u,v)=(u+v)(u-v)/4+((u-v)^2)/4

由于函数变量符号可以随便写

所以f(x,y)=(x+y)(x-y)/4+((x-y)^2)/4

df(x,y)=(x-y/2)dx-x/2dy