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

2025-01-24 05:27:40
推荐回答(1个)
回答1:

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]