求y=arccos(x+1/x-1)导数

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求y=arccos(x+1/x-1)导数求y=arccos(x+1/x-1)导数求y=arccos(x+1/x-1)导数y=arccos(x+1)/(x-1)y''=-1/√[1-((x+1)/(x-1

求y=arccos(x+1/x-1)导数
求y=arccos(x+1/x-1)导数

求y=arccos(x+1/x-1)导数
y=arccos(x+1)/(x-1)
y'=-1/√[1-((x+1)/(x-1))^2] * ((x+1)/(x-1))'
y'=2/√[1-((x+1)/(x-1))^2] * (1/(x-1)^2)
因为:1-((x+1)/(x-1))^2>0
(x-1)^2-(x+1)^2>0,即:-4x>0,x

令x+1/x-1=g(x)
就化为了复合函数求导、
y'=-1/根号下(1-g^2(x))乘以g(x)的导数