#### Answer

\[ {s^,}\,\left( t \right) = 2\,\left( {{t^2} + {e^t}} \right)\,\left( {2t + {e^t}} \right)\]

#### Work Step by Step

\[\begin{gathered}
s = \,{\left( {{t^2} + {e^t}} \right)^2} \hfill \\
Find\,\,the\,\,derivative\,\,of\,\,the\,\,\,function \hfill \\
{s^,} = \,\,{\left[ {\,{{\left( {{t^2} + {e^t}} \right)}^2}} \right]^,} \hfill \\
Use\,\,the\,\,general\,\,\,power\,\,rule \hfill \\
{s^,} = 2\,{\left( {{t^2} + {e^t}} \right)^{2 - 1}}\,{\left( {{t^2} + {e^t}} \right)^,} \hfill \\
Then \hfill \\
{s^,}\,\left( t \right) = 2\,\left( {{t^2} + {e^t}} \right)\,\left( {2t + {e^t}} \right) \hfill \\
\end{gathered} \]