求由参数方程x=(1+lnt)/t^2,y=(3+2lnt)/t确定的函数y=y(x)的dy/dx,d^2y/dx^2

求由参数方程x=(1+lnt)/t^2,y=(3+2lnt)/t确定的函数y=y(x)的dy/dx,d^2y/dx^2
求由参数方程x=(1+lnt)/t^2,y=(3+2lnt)/t确定的函数y=y(x)的dy/dx,d^2y/dx^2

求由参数方程x=(1+lnt)/t^2,y=(3+2lnt)/t确定的函数y=y(x)的dy/dx,d^2y/dx^2
dx/dt=[1/t*t^2-(1+lnt)*2t]/t^4=-(1+2lnt)/t^3
dy/dt=[2/t*t-(3+2lnt)]/t^2=-(1+2lnt)/t^2
因此y'=dy/dx=(dy/dt)/(dx/dt)=t
dy'/dt=1
d^2y/dx^2=d(y')/dt/(dx/dt)=-t^3/(1+2lnt)