Question

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

Answer 1

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