高数导数问题参数方程求二次导数时,对dy/dx再求导变成(d^2y)/dx^2=d*dy/dx^2这里d与y拆开后d代表

dy/dx是一阶导数
d^2y/dx^2是二阶导数
d^2y/dx^2=dy'/dx
y'=dy/dx
x=a(t-sint)
y=a(1-cost)
一阶导数
y'=dy/dx
=da(1-cost)/da(t-sint)
=[a(1-cost)]'/[a(t-sint)]'
=asint/a(1-cost)
=sint/(1-cost)
二阶导数
y''=dy'/dx
=d(sint/(1-cost))/da(t-sint)
=[(sint/(1-cost)]'/[a(t-sint)]'
=[(cost(1-cost)-sint(sint))/(1-cost)^2]/a(1-cost)
=[(cost-(cost)^2-(sint)^2)/(1-cost)^2]/a(1-cost)
=(cost-1)/a(1-cost)^3
= -1/a(1-cost)^2
注意：楼上的dy/dt=a(1+sint) 出问题了,应该是dy/dt=asint

解:dx/dt=a(1-cost)
dy/dt=a(1+sint)
dy/dx=(dy/dt)/(dt/dx)=a(1+sint)/a(1-cost)=(1+sint)/(1-cost)
d(dy/dx)/dx=[d(dy/dx)/dt]*(dt/dx)=[(cost-sint-1)/(1-cost)^2]/[a(1-cost)]=(cost-sint-1)/[a(1-cost)^3]

这里d与y拆开后d代表取微分。因为二次导数可以表示成：[d(dy/dx)]/dx,小括号里的是一个函数，外面的d表示对小括号里的函数取微分。
例子的解答如下：
dx/dt=a(1-cost)
dy/dt=a*sint
dy/dx=(a*sint)/a(1-cost)=sint/(1-cost)，这就是小括号里的函数，是关于中间变量t的函数
再对dy/dx对t...

还是导数。其实应该是：d(dy/dx)/dx
这样子才是二阶导的意义。
dx/dt=a(1-cost)
dy/dt=a(1+sint)
dy/dx=(dy/dt)/(dt/dx)=a(1+sint)/a(1-cost)=(1+sint)/(1-cost)
d(dy/dx)/dx=[d(dy/dx)/dt]*(dt/dx)=[(cost-sint-1)/(1-cost)^2]/[a(1-cost)]=(cost-sint-1)/[a(1-cost)^3]