Show that

\[
\int_{-\infty}^{\infty} t x^{*}(t) x^{\prime}(t) d t=-\int_{-\infty}^{\infty} f X^{*}(f) X^{\prime}(f) d f
\]

where \(X(f)\) is the FT of \(x(t)\), and \(x^{\prime}(t)\) is its derivative with respect to time. The function \(X^{\prime}(f)\) is the derivative of \(X(f)\) with respect to frequency.