Consider the linear, time$-$invariant system in Figure P$5\mathrm{.}4,$ which is composed of a cascade of two LTI systems. $u(t)$ is a unit step signal and $s(t)$ is the step response of system $L.$

Using the fact that the overall response of LTI systems in cascade is independent of the order in which they are cascaded, show that the impulse response of system $L$ is the derivative of its step response, i$.$e$.,$

$h(t)=\frac{ds(t)}{dt}$