Question

数学，求4个函数的导数，求详解

Answer 1

因为这里书写不便，故将我的答案做成图像贴于下方，谨供楼主参考（若图像显示过小，点击图片可放大）

Answer 2

∂Q/∂x = ∂[y/(x+y)^2]/∂x = -2y(x+y)^3,
∂P/∂y = ∂[(x+2y)/(x+y)^2]/∂y
= [2(x+y)^2-2(x+2y)(x+y)]/(x+y)^4 = -2y/(x+y)^3
则 [(x+2y)dx+ydy]/(x+y)^2 是函数 u(x,y) 的全微分，即它存在原函数。
u(x,y) = ∫<x0, x> P(x, y0)dx + ∫<y0, y> Q(x, y)dy,
此时不能取 x0 = y0 = 0, 不妨取 x0 = 1， y0 = 0
u(x,y) = ∫<1, x> (1/x)dx + ∫<0, y> [y/(x+y)^2]dy
= ln|x| + x/(x+y)-1+ln|x+y|-ln|x| = x/(x+y)+ln|x+y|-1 = C1
则原函数是 x/(x+y)+ln|x+y| = C

Answer 3

正在计算，等下发出来

追问

好的呢

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