数学二阶导数由参数方程｛x=sinty=cos2t确定的y是x的函数y=y(x)的二阶导数（d^2y）/(dx^2)

Question

数学二阶导数
由参数方程｛x=sint
y=cos2t
确定的y是x 的函数y=y(x)的二阶导数（d^2y）/(dx^2)

Answer 1

先求一阶导数：
dx/dt = cost
dy/dt = -2sin2t dy/dx = dy/dt ÷ dx/dt = -2sin2t/cost = -4sint cost / cost = -4sint ;
再求二阶导数：
(dy/dx)/dt = -4cost
dx/dt = cost
(d^2y)/(dx^2) = (dy/dx)/dt ÷ dx/dt = -4cost / cost =-4