$(10$ points$)$ Consider a general transfer function $G(s)=\frac{Y(s)}{U(s)}.$ Show that, for any transfer function $G(s)$ subject to an input $u(t),$ the relation between the step response $y_s$ and impulse response $y_i$ in the time domain is given by:

$\frac{d}{dt}{y}_s(t)=y_i(t)$