d²y/dx² is just the derivative of dy/dx, when dy/dx is defined as a function of x. But in this case, it is defined as a function of t, so we need to use chain rule

x = e^t dx/dt = e^t ------> dt/dx = e^(−t)

y = te^(−t) dy/dt = e^(−t) − t e^(−t) = −e^(−t) (t − 1)