由参数方程x=1+t2,y=t-arctant所确定的函数y=y(x)的二阶导数

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x't=2t
y't=1-1/(1+t^2)=t^2/(1+t^2)
y'=dy/dx=y't/x't=t/[2(1+t^2)]
d^y/dx^2=d(y')/dx=d(y')/dt/x't=1/2*[1+t^2-2t^2]/(1+t^2)^2/(2t)=(1-t^2)/[4t(1+t^2)^2]