设由参数方程﹛x=t^2/2,y=1-t,确定的函数为y=y(x),求d^2y/dx^2

Question

设由参数方程﹛x=t^2/2,y=1-t,确定的函数为y=y(x),求d^2y/dx^2

Answer 1

X=t^2/2
Y=1-t
dy/dx=(dy/dt)/(dx/dt)
=(-1)/t
=-1/t
d^2y/dx^2=d/dx(dy/dx)
=(d/dt(dy/dx))/(dx/dt)
=(1/t^2)/t
=1/t^3