求下列参数方程所确定的函数的三阶导数d^3y/dx^3x=In(1+t^2)y=t-arctant

Question

求下列参数方程所确定的函数的三阶导数d^3y/dx^3 x=In(1+t^2) y=t-arctant

Answer 1

dy/dt=1-1/(1+t²)=t²/(1+t²)
dx/dt=2t/(1+t²)
dy/dx=t/2
d²y/dx²=(1/2)/[dx/dt]=(1+t²)/4t
d^3y/dx^3 =[t^4-1]/[8t^3]