dx/dt=6t+2,dy/dt=（3t+1）sin（t^2）,求d^2y/dx^2d^2y/dx^2不是直接对dy/dx求导吗_数学解答

dx/dt=6t+2,dy/dt=（3t+1）sin（t^2）,求d^2y/dx^2
d^2y/dx^2不是直接对dy/dx求导吗

人气：385 ℃　时间：2020-01-26 07:12:22

解答

dy/dx＝（3t+1）sin（t²）/(6t+2)=1/2sin（t²）
dt²y/dx²
=d [1/2sin（t^2)]/dx
=t*cos(t²)*dt/dx
=t*cos(t²)/(6t+2)