Question

x=e^(-t);y=te^t 则d^2y/dx^2=

Answer 1

x=e^(-t);y=te^t

所以

dx/dt=-e^(-t)

dy/dt=e^t+te^t

dy/dx=(1+t)e^t/(-e^(-t))=-(1+t)e^2t

d(dy/dx)/dt=-e^(2t)-2(1+t)e^2t=-(2t+3)e^2t

所以

d^2y/dx^2=【-(2t+3)e^2t】/【-e^(-t)】=(2t+3)e^3t