Differentiation
x(t) = $ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $
diffrentiate both sides
x'(t) = d($ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $)
x(t) = $ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $
diffrentiate both sides
x'(t) = d($ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $)