#### Answer

\[{y^,} = 18{x^2} - 6x + 4\]

#### Work Step by Step

\[\begin{gathered}
y = \,\left( {3{x^2} + 2} \right)\,\left( {2x - 1} \right) \hfill \\
Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{y^,} \hfill \\
{y^,} = \,{\left( {3{x^2} + 2} \right)^,}\,\left( {2x - 1} \right) + \,{\left( {2x - 1} \right)^,}\,\left( {3{x^2}2} \right) \hfill \\
Then \hfill \\
{y^,} = \,\left( {6x} \right)\,\left( {2x - 1} \right) + \,\left( 2 \right)\,\left( {3{x^2} + 2} \right) \hfill \\
Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\
{y^,} = 12{x^2} - 6x + 6{x^2} + 4 \hfill \\
{y^,} = 18{x^2} - 6x + 4 \hfill \\
\hfill \\
\end{gathered} \]