第1个回答 2012-04-10
你好！
这两道题的详细过程见插入的图片 ，点击一次图片后出现一个小图片，再点击一次便出现放大的图片。
第2个回答 2012-04-06
1
(x+y)/(x-y)=1+2y/(x-y)
[(x+y)/(x-y)]'x=2y'/(x-y) -2y(1-y')/(x-y)^2
[(x+y)/(x-y)]'y=2/(x-y)+2y(-1)/(x-y)^2 1+(x+y)^2/(x-y)^2=2x^2+2y^2/(x-y)^2
dz=[(dy/dx)(x-y)-y(1-dy/dx)]/(x^2+y^2) *dx + (x-2y)/(x^2+y^2) dy
2
[(x+y)/(1-xy)]'x=(1+y')/(1-xy)-(x+y)(-y-xy')/(1-xy)^2
[(x+y)/(1-xy)]'y=(1+x')/(1-xy)-(x+y)(-x-x'y)/(1-xy)^2
1+(x+y)^2/(1-xy)^2=[(x+y)^2+(1-xy)^2]/(1-xy)^2
dz=[(1+dy/dx)(1-xy)-(x+y)(-y-xdy/dx)]/[(1-xy)^2+(x+y)^2] dx
+ [(1+dx/dy)(1-xy)-(x+y)(-x-ydx/dy)]/[(1-xy)^2+(x+y)^2] dy追问
(x+y)/(x-y)=1+2y/(x-y)
[(x+y)/(x-y)]'x=2y'/(x-y) -2y(1-y')/(x-y)^2
[(x+y)/(x-y)]'y=2/(x-y)+2y(-1)/(x-y)^2 1+(x+y)^2/(x-y)^2=2x^2+2y^2/(x-y)^2
dz=[(dy/dx)(x-y)-y(1-dy/dx)]/(x^2+y^2) *dx + (x-2y)/(x^2+y^2) dy
2
[(x+y)/(1-xy)]'x=(1+y')/(1-xy)-(x+y)(-y-xy')/(1-xy)^2
[(x+y)/(1-xy)]'y=(1+x')/(1-xy)-(x+y)(-x-x'y)/(1-xy)^2
1+(x+y)^2/(1-xy)^2=[(x+y)^2+(1-xy)^2]/(1-xy)^2
dz=[(1+dy/dx)(1-xy)-(x+y)(-y-xdy/dx)]/[(1-xy)^2+(x+y)^2] dx
+ [(1+dx/dy)(1-xy)-(x+y)(-x-ydx/dy)]/[(1-xy)^2+(x+y)^2] dy追问
诶，答案不对。
第一个答案是，dz=(xdy-ydx)/(x²+y²)
第二个答案是，dz=dx/(1+x^2)+dy/(1+y^2)
第3个回答 2012-04-04
1、dz=(xdy-ydx)/(x²+y²)
2、dz=[(1+y²)dx+(1+x²)dy]/[(1-xy)²+(x+y)²]追问
2、dz=[(1+y²)dx+(1+x²)dy]/[(1-xy)²+(x+y)²]追问
第一个答案是对的，可有详解？
第二个答案不对，答案是dx/(1+x^2)+dy/(1+y^2)
dz=[(1+y²)dx+(1+x²)dy]/[(1-xy)²+(x+y)²]=dx/(1+x^2)+dy/(1+y^2)
第4个回答 推荐于2016-11-04
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