Question

微积分：求参数方程的二阶导数,

Answer 1

1) dx/dt=a,dy/dt=at+b

y'=(at+b)/a=t+b/a

dy/dt=1

y"=1/a

2) dx/dt=3a(cost)^2*(-sint)

dy/dt=3a(sint)^2*cost

y'=-sint/cost=tant

dy'/dt=(sect)^2

y"=dy/dt/(dx/dt)=-(sect)^2/[3a(cost)^2tsint]=-(sect)^4/(3asint)

3)dx/dt=2t

dy/dt=-sint

y'=-sint/(2t)

dy'/dt=-1/2*(tcost-sint)/t^2=(sint-tcost)/(2t^2)

y"=dy/dt/(dx/dt)=(sint-tcost)/(4t^3)