设z=xy/(x^2-y^2),求当x=2,y=1,Δx=0.01,Δy=0.03时的全微分_数学解答

设z=xy/(x^2-y^2),求当x=2,y=1,Δx=0.01,Δy=0.03时的全微分

人气：494 ℃　时间：2020-06-24 08:53:35

解答

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.