Finding the inverse laplace transform of $s$

Question

How do I find the inverse laplace transform of $s$, i.e. $$L^{-1}\{s\}=\ ?$$

Answer 1

One would have a hard time finding such a function since Laplace transforms of functions go to zero at infinity and Laplace transforms of measures are bounded.

Answer 2

$\mathcal{L}^{-1}\{s\}=\delta'(t)$. More generally:

$\forall n\in\mathbb{Z},~\mathcal{L}^{-1}\{s^n\}=\delta^{(n)}(t)$.