x=f'(t) y=tf'(t)-f(t)的三阶导数?
问题描述：
x=f'(t) y=tf'(t)-f(t)的三阶导数?
二阶已知为1/f"(t)
答
x=f'(t)
y=tf'(t)-f(t)
dy/dx
=[dy/dt]/[dx/dt]
=[f'(t)+tf''(t)-f'(t)]/f''(t)
=t
d^2y/dx^2
=[d(dy/dx)/dt]/[dx/dt]
=1/f''(t)
d^3y/dx^3
=[d(d^2y)/dt]/[dx/dt]
=[d(1/f''(t))/dt]/f''(t)
=[-f'''(t)/(f''(t))^2]/f''(t)
=-f'''(t)/[f''(t)]^3