Answer
$\dfrac{e^{st} s}{(2s-e^{st}t)}$
Work Step by Step
We have: $e^{st}=s^2$
We differentiate both sides with respect to $t$.
$e^{st} (s+t \dfrac{ds}{dt})=2s \dfrac{ds}{dt} \\ (e^{st}t-2s) \dfrac{ds}{dt}=-e^{st} s$
Therefore, $ \dfrac{ds}{dt}=\dfrac{e^{st} s}{(2s-e^{st}t)}$
