Question

设f(t)是二次可微函数且f''(t)不等于0 x=f'(t),y=tf'(t)-f(t),求dy/dx,d^2y/dx

Answer 1

dx/dt=f''(t)

dy/dt=f'(t)+tf''(t)-f'(t)=tf''(t)

dy/dx=(dy/dt)/(dx/dt)=1/t

d^2y/dt^2=f''(t)+tf'''(t)

d^2y/dx^2=(d^2y/dt^2)/[(dx/dt)*(dx/dt)]=1/f''(t)+tf'''(t)/[f''(t)^2]