I have an exercise, I graphically understood that the relationship is true, but I have a little doubt on how to prove it. $$ \frac{d\Pi(t)}{dt} = \delta\left(t + \frac{1}{2}\right) - \delta\left(t - \frac{1}{2}\right) $$ where $ \delta(t) $ is the Dirac impulse, and $ \Pi=\{ 1 $ if $|t| \leq \frac{1}{2} $ , 0 else $ \}$
I have to prove that this relationship is true. Can u help me? Thanks!