Find d^2y/dx^2 where x=e^t, y=te^-t

Answer 1

y' = (dy/dt) / (dx/dt) = (1-t)e^-t / e^t = (1-t)e^(-2t)
y" = dy'/dx = (dy'/dt) / (dx/dt) = (2t-3)e^(-2t) / e^t = (2t-3)e^(-3t)