Well as I wrote here i(t) (given by me) is the response to u(t) therefore i(t) = u(t)*h(t) where h(t) is the impulse response, so we can calculate h(t) in the frequency domain as: H(s) = sI(s) but this creates a confusion since if the response of u(t) is i(t) the response to D(t) (A unit impulse = du(t)/dt ) should be di(t)/dt which becomes in the s domain as: sI(s) - i(0+) hence we get 2 different answers. Stretching this to the basics we have Laplace of u(t) = 1/s so the Laplace for a unit impulse D(t) should be (from the differentiation rule) = s.(1/s) - u(0+) = 1 - 1 = 0. But its simply taken s.(1/s) = 1. Why is this? Any help would be appreciated.