设=dfrac (y)(f({x)^2-(y)^2)},其中f为可导函数.验证=dfrac (y)(f({x)^2-(y)^2)}.

设 =dfrac (y)(f({x)^2-(y)^2)} ,其中f(u)为可导函数,验证-|||-.dfrac (1)(x)dfrac (dz)(partial

7.设 =dfrac (y)(f({x)^2-(y)^2)} 其中f为可导函数,验证: dfrac (1)(x)dfrac (partial z)(partia

3.设 =dfrac (y)(f({x)^2-(y)^2)} ,其中f为可微函数,验证-|||-dfrac (1)(x)dfrac (partial z)(pa

设=dfrac (2x)({x)^2-(y)^2} ，则 =dfrac (2x)({x)^2-(y)^2}=dfrac (2x)({x)^2-(y)^2}___

[题目]设 (x-y,y|x)=(x)^2-(y)^2 求f(x,y)

12.设函数 (x,y)=2((y-{x)^2)}^2-(y)^2-dfrac (1)(7)(x)^7 。(1)求f(x,y)的极值,并证明函数f(x,y)-|

求下列各函数的定义域，画出定义域的图形，并说明这是何种点集：(1)f(x，y)=dfrac({x)^2+(y)^2}({x)^2-(y)^2}(2)f(x，y)

7.函数 (x,y)=dfrac (arcsin (3-{x)^2-(y)^2)}(x-{y)^2} 的定义域为7.函数 (x,y)=dfrac (arcsin

设 (x+y,x-y)=2((x)^2+(y)^2)(e)^(x^2-{y)^2}, 则 _(x)(x,y)-(f)_(y)(x,y)= __

2.设 (xy,x+y)=(x)^2+(y)^2+xy (其中, =xy =x+y), 则 dfrac (partial f)(partial u)+dfrac