作业帮设f(x+y,x-y)=x^2+xy,求f(x,y)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 04:11:01
设f(x+y,x-y)=x^2+xy,求f(x,y)
设f(x+y,x-y)=x^2+xy,求f(x,y)
设f(x+y,x-y)=x^2+xy,求f(x,y)
设f(x+y,x-y)=x^2+xy
设u=x+y,v=x-y
则x=（u+v）/2,y=(u-v)/2
所以f(u,v)=(u+v)^2/4+(u+v)(u-v)/4
所以f(x,y)=(x+y)^2/4+(x+y)(x-y)/4=(x^2+xy)/2
令a=x+y,b=x-y
两式相加a+b=2x,x=(a+b)/2,y=a-x=a-(a+b)/2=(a-b)/2
代入
f(a,b)=[(a+b)/2]^2+[(a+b)/2][(a-b)/2]
=[(a+b)^2]/4+[(a+b)(a-b)]/4
=2a(a+b)/4=a(a+b)/2
∴f(x,y)=x(x+y)/2
设f(x+y,x-y)=x^2+xy,求f(x,y)
设函数f(xy,x+y)=x^2+y^2+xy,求∂f(x,y)／∂x和∂f(x,y)／∂y
设F(xy,y^2/x)=x^2+y^2,求F（y^2/x,xy）
设函数f(x,y)=xy/根号x^2+y^2,求limf(x,y)x,y趋于0
设f(x-y,x+y)=xy 求f(x,y)
设函数f(x,y)=(2xy)除以（x^2+y^2)求f（1,y/x)
f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
f(x+y,x-y)=2xy(x-y),求f(x,y)
设f（x+y,xy）=x^2+y^2,则f（x,y）
f(xy,x-y)=x^2-xy+y^2.求f(x,y)
设f(x+y,xy)=x^2+y^2-xy,则（∂f(x,y)）/∂y=
二元函数 设(x,y)=3xy/(x^2+y^2),求f(y/x,1)
设f(x-y,y/x)=xy,则f(xy,x+y)等于什么
设f(x-y,y/x)=xy,则f(xy,x+y)等于什么
y'=-2xy;求f(x).
f(x^2-y^2,x-y)=x+y+x^2-xy,求f'(x,y)对y求导
f(x,y)=xy+e^x x arctanx/y ,求f(x+y,x-y)
设f(x,y)=xe^y+xy,则f(x+y,x-y)=