Question

求导数，化简过程详细点

Answer 1

y=arctan[(x^2+1)/(x^2-1)]^(1/2)

y'=1/{1+[(x^2+1)/(x^2-1)]}*{[(x^2+1)/(x^2-1)]^(1/2)}'
=[2x^2/(x^2-1)]*(1/2)[(x^2+1)/(x^2-1)]^(1/2-1)*[(x^2+1)/(x^2-1)]'
=[x^2/(x^2-1)]*[(x^2+1)/(x^2-1)]^(-1/2)*[(x^2+1)'(x^2-1)-(x^2+1)(x^2-1)']/(x^2-1)^2
=[x^2/(x^2-1)]*[(x^2+1)/(x^2-1)]^(-1/2)*[2x(x^2-1)-(x^2+1)2x]/(x^2-1)^2
=[x^2/(x^2-1)]*[(x^2+1)/(x^2-1)]^(-1/2)*(-4x)/(x^2-1)^2
=-4x^3(x^2+1)^(-1/2)*(x^2-1)^(-7/2)
=-4x^3/[(x^2+1)^(1/2)*(x^2-1)^(7/2)]