I 'll be asking some S&S related questions here, have a look at them when you get the time:

Q1: Prove that δ'(-t)=-δ'(t)

As hinted, I attempted this by using \(\int \phi (t) f_1(t) dt =\int \phi (t) f_2(t) dt \Leftrightarrow f_1(t)=f_2(t)\)

So,

\(\int_{-\infty}^{\infty} \phi(t) (- \delta ' (t)) dt=\int_{-\infty}^{\infty} \phi '(t) \delta (t) dt=\phi'(0)\)

and

\(\int_{-\infty}^{\infty} \phi(t) \delta ' (-t) dt=-\int_{\infty}^{-\infty} \phi(-\tau) \delta ' (\tau) d\tau\)

but I can't see the last step, to get to the same result. Any hints?