Answer

We know from derivative of transforms

\[ \begin{aligned} \diffone{F}(s) &= -L\roundbr{tf(t)}\newline \implies L\roundbr{\frac{1}{2}te^{-3t}} &= -\frac{1}{2} \frac{d}{ds} L\roundbr{e^{-et}}\newline &= \frac{-1}{2} \frac{d}{ds}\frac{1}{s+3}\newline &= \frac{1}{2}\frac{1}{\roundbr{s+3}^{2}} \end{aligned} \]