求y=arctan(x+1/x-1)的导数

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求y=arctan(x+1/x-1)的导数求y=arctan(x+1/x-1)的导数求y=arctan(x+1/x-1)的导数y=arctan(x+1)/(x-1)y''=1/[1+(x+1)^2/(x

求y=arctan(x+1/x-1)的导数
求y=arctan(x+1/x-1)的导数

求y=arctan(x+1/x-1)的导数
y=arctan(x+1)/(x-1)
y'=1/[1+(x+1)^2/(x-1)^2]*[(x+1)/(x-1)]'
=1/[1+(x+1)^2/(x-1)^2]*[(x-1)-(x+1)]/(x-1)^2
=-2/[(x+1)^2+(x-1)^2]
=-1/(x^2+1)