答案啥意思，让你求(0,1)点全微分，不是求(0,0)点全微分啊，为啥要带入z=

Question

答案啥意思，让你求(0,1)点全微分，不是求(0,0)点全微分啊，为啥要带入z=-1？

Answer 1

dz=d(xy/(x^2-y^2)=d(xy)/(x^2-y^2)-xy/(x^2-y^2)^2*d(x^2-y^2)=(ydx+xdy)/(x^2-y^2)-xy/(x^2-y^2)^2（2xdx-2ydy)=(y/(x^2-y^2)-2x^2y/(x^2-y^2)^2)dx+(x/(x^2-y^2)-2xy^2/(x^2-y^2)^2)dy,r然后楼主自己代吧。。。本回答被网友采纳

Answer 2

照题目看是个错题，当x=0,y=0时用z=-1代人隐函数方程不成立，说明z(0,0)=-1不可能成立。疑该条件应为z(0,1)=-1