By using the quotient rule, I get -3e^t for the numerator. The problem is the denominator: (t+3e^t)^2 I don't believe I'm foiling the denominator correctly.
Follow Math Help Forum on Facebook and Google+
$\displaystyle \left(\displaystyle\frac{1}{t+3e^t}\right)'=-\displaystyle\frac{(t+3e^t)'}{(t+3e^t)^2}=-\displaystyle\frac{1+3e^t}{(t+3e^t)^2}$