微积分高阶导数问题,求参数方程所确定的函数的二阶导数,x=f '(t)y=t f '(t)+f(t)其中f''(t)存在

dx/dt = f''(t)
dy/dt = f'(t) + tf''(t) + f'(t) = 2f'(t) + tf''(t)
dy/dx = [2f'(t) + tf''(t)]/f''(t) = 2f'(t)/f''(t) + t
d²y/dx² = [d(dy/dx)/dt][dt/dx]
= {2f''(t)/f''(t) - 2f'(t)f'''(t)/[f''(t)]² + 1}[1/f''(t)]
= [2 - 2f'(t)f'''(t)/[f''(t)]² + 1][1/f''(t)]
= 3/f''(t) - 2f'(t)f'''(t)/[f''(t)]³
题目应该有误.

dy/dx=(2f'(t)+t*f''(t))/(f''(t))