Question

已知函数f(x+y,x-y)=x^2-y^2,则偏f(x,y)/偏x+偏f(x,y)/偏y=? 求详细过程

Answer 1

偏f(x,y)/偏x=2x
偏f(x,y)/偏y=-2y

偏f(x,y)/偏x+偏f(x,y)/偏y
=2x-2y

追问

答案是x+y啊。。

追答

抱歉，看错了
f(x+y,x-y)=x^2-y^2=(x+y)(x-y)
所以，f(x,y)=xy
所以：
偏f(x,y)/偏x=y
偏f(x,y)/偏y=x

偏f(x,y)/偏x+偏f(x,y)/偏y
=x+y

Answer 2

f(x+y,x-y)=x^2-y^2=(x+y)(x-y)
f(x,y)=xy
偏f(x,y)/偏x+偏f(x,y)/偏y=y+x