Answer
\[{g^,}\,\left( t \right) = 36{t^3} + 24t\]
Work Step by Step
\[\begin{gathered}
g\,\left( t \right) = \,{\left( {3{t^2} + 2} \right)^2} \hfill \\
Write\,\,as\,a\,\,product\,\, \hfill \\
g\,\left( t \right) = \left( {3{t^2} + 2} \right)\left( {3{t^2} + 2} \right) \hfill \\
Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{g^,}\,\left( t \right) \hfill \\
{g^,}\,\left( t \right) = \,\left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} + \left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} \hfill \\
{g^,}\,\left( t \right) = 2\left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} \hfill \\
Then \hfill \\
{g^,}\,\left( t \right) = 2\left( {3{t^2} + 2} \right)\,\left( {6t} \right) \hfill \\
Multiplying \hfill \\
{g^,}\,\left( t \right) = 12t\left( {3{t^2} + 2} \right) \hfill \\
{g^,}\,\left( t \right) = 36{t^3} + 24t \hfill \\
\end{gathered} \]
