(a) The system response requires memory. Hence, it is dynamic.
(b) The output depends on the present input only. Hence, it is causal.
(c) The output due to the delayed input is not the same as the delayed output. Hence, it is time variant.
(d) The weighted sum of the output is the same as output due to weighted sum of the input. Hence, the system is linear.
(e) Since \(\frac{d}{d t}\left(e^{-2 t} x(t)ight)\) is bounded \(y(t)\) is also bounded, and hence the system is stable.

\[
y(t)=\frac{d}{d t}\left[e^{-2 t} x(t)ight]
\]