Answer
$-\frac{(t+2)^2}{t^2e^t}$
Work Step by Step
$\frac{d}{dt}\frac{4+t}{te^t}$
$=\frac{te^t\frac{d}{dt}(4+t)-(4+t)\frac{d}{dt}(te^t)}{(te^t)^2}$
$=\frac{te^t*1-(4+t)(t\frac{d}{dt}e^t+e^t\frac{d}{dt}t)}{(te^t)^2}$
$=\frac{te^t-(4+t)(te^t+e^t*1)}{(te^t)^2}$
$=\frac{te^t-e^t(4+t)(t+1)}{(te^t)^2}$
$=\frac{e^t(t-(t^2+5t+4))}{e^t(t^2e^t)}$
$=-\frac{t^2+4t+4}{t^2e^t}$
$=-\frac{(t+2)^2}{t^2e^t}$
