Solution
= Solution
The <derivative> of a distribution is defined by integration by parts. Therefore
$$
\boxed{\int_{-\infty}^{\infty}f(t)\delta'(t)dt
=-\int_{-\infty}^{\infty}f'(t)\delta(t)dt
=-f'(0).}
$$
= Solution
The <derivative> of a distribution is defined by integration by parts. Therefore
$$
\boxed{\int_{-\infty}^{\infty}f(t)\delta'(t)dt
=-\int_{-\infty}^{\infty}f'(t)\delta(t)dt
=-f'(0).}
$$