If $g(t)=\frac{t^2+1}{e^t},$ then $g^{\text{'}}(t)=$

Select one:

$\frac{-t^2+2t-1}{e^{2t}}$

$\frac{-t^2{e}^t+2t{e}^t-e^t}{e^{2t}}$

$\frac{t^2{e}^t+2t{e}^t+e^t}{e^{2t}}$

$\frac{-t^2{e}^t+2t{e}^t-e^t}{e^t}$

$\frac{-t^2{e}^t+t{e}^t-e^t}{e^{2t}}$

If $g(t)=\frac{t^2+1}{e^t},$ then $g^{\text{'}}(t)=$

Select one:

$\frac{-t^2+2t-1}{e^{2t}}$

$\frac{-t^2{e}^t+2t{e}^t-e^t}{e^{2t}}$

$\frac{t^2{e}^t+2t{e}^t+e^t}{e^{2t}}$

$\frac{-t^2{e}^t+2t{e}^t-e^t}{e^t}$

$\frac{-t^2{e}^t+t{e}^t-e^t}{2t}$