Question

求到了dy/dx，那么这个d^2y/dx^2怎么算出来的?

公式也看不懂

Answer 1

Answer 2

d^2y/dx^2
=d/dx( dy/dx)
=d/dt( dy/dx) / (dx/dt) ( chain rule )

追问

比如这道题

追答

x= t- 1/t
dx/dt = 1 +1/t^2 = (t^2+1)/t^2
y=(1/2)t^2 +lnt
dy/dx = t + 1/t = (t^2 +1)/t
dy/dx = (dy/dx)/(dx/dt) = t
d^2y/dx^2
=d/dt ( dy/dx ) / (dx/dt)
=d/dt ( dy/dx ) / [(t^2+1)/t^2]
=d/dt ( t ) / [(t^2+1)/t^2]
=1/[(t^2+1)/t^2]
=t^2/(t^2+1)

Answer 3

d^2y/dx^2就是dy/dx的导函数