[What is the impulse response?]

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.

[What is the impulse response?]

Hello,
I have a question regarding Network Analysis.
Suppose we are given that the response to a step input at t=0 to a network is given as say
i(t) = -2exp(-t) + 4exp(-3t)

Then what is the impule response of the network and how can it be calculated??
Any suggestions are welcome.