what is tha derivative of an impulse function?

Answer 1

What is an impulse function? Are you talking about the dirac delta function or like a unit step function? If it is a unit step function, then derivative would zero along where it is continuous and then undefined where there is a step on the edges.

For example, if I have
f(x)=
1 if 0 0 if 1 1 if 2 etc...

then
f'(x)=
undefined if x is an integer
0 otherwise

Answer 2

Derivative is defined for continuous functions only. The unit impulse (Kronecker Delta) is not a continuous function. The function can be integrated, however, and the integral (if the impulse is at x=0) is 0 from -inf to 0, 1 from 0 to inf. (Unit step function).
Goto derivative section of MIT university and u'll learn hell lottof fundas

Answer 3

Derivative is defined for continuous functions only. The unit impulse (Kronecker Delta) is not a continuous function. The function can be integrated, however, and the integral (if the impulse is at x=0) is 0 from -inf to 0, 1 from 0 to inf. (Unit step function).

Dirac Delta is also an impulse function, and it apparently can be differentiated. See http://en.wikipedia.org/wiki/Impulse_function