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
问题描述:
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
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)