参数方程的二阶导数求解，哪位高手帮个忙啊

Question

如题所述

Answer 1

dx/dt=(-1-2lnt)/(t^3)
dy/dt=(-1-2lnt)/(t^2)

dx/dy=(dx/dt)/(dy/dt)=1/t
d(dx/dy)/dt= -1/(t^2)
d^2x/dy^2=(d(dx/dy)/dt)/(dy/dt)= {-1/(t^2)}/{(-1-2lnt)/(t^2)}=1/(1+2lnt)
由y=3知道t=1
所以t=1代入后得结果d^2x/dy^2=1

Answer 2

1 dx/dt = -2/t^3(1+lnt) + (1/t^2)*(1/t) = -(1/t^3)(1+lnt)
dy/dt = (-1/t^2)(3+2*lnt)+(1/t)*(2/t) = -(1/t^2)(1+2*lnt)
dx/dy =(dx/dt )/(dy/dt) =1/t
2 d2x/dy2 = (d(dx/dy )/dt) * (dt/dy) = (-1/t^2)/[-(1/t^2)(1+2*lnt)] = 1/(1+2*lnt)
易知 y=3 ，t=1
带入得d2x/dy2 =1