求解x=ln(1 t^2)和y=t-arctanx的二阶导数

2025-01-24 05:47:39
推荐回答(1个)
回答1:

x=ln(1+t²)
y=t-arctant
dx/dt=2t/(1+t²)
dy/dt=1-1/(1+t²)=t²/(1+t²)
∴dy/dx=t/2
∴d²y/dx²=½/[2t/(1+t²)]=(1+t²)/4t
(y=t-arctanx,将x=ln(1+t²)代入,y=t-arctan[ln(1+t²)],计算过程一样)