The input and impulse response of a continuous$-$time LTI system are given below.

$x(t)=u(t-3)-u(t-5)$ and $h(t)=e^{-3t}u(t),\frac{d}{dt}x(t)**h(t)$ The result of the operation $x(t)$

$**h(t)$ is equal to which of the following?

A$)y(t)=e^{-3(t-3)}u(t-3)-e^{-3(t-5)}u(t-5)$

B$)y(t)=e^{-3(t-3)}u(t-3)+e^{-3(t-5)}u(t-5)$

C$)y(t)=e^{-3(t-3)}u(t+3)-e^{-3(t-5)}u(t-5)$

D$)y(t)=e^{-3(t-3)}u(t-3)-e^{-3(t-5)}u(t+5)$

E$)y(t)=e^{-3(t+3)}u(t-3)-e^{-3(t-5)}u(t-5)$