#### Answer

\[{y^,} = 60{x^2} + 30x - 4\]

#### Work Step by Step

\[\begin{gathered}
y = \,\left( {5{x^2} - 1} \right)\,\left( {4x + 3} \right) \hfill \\
Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{y^,} \hfill \\
{y^,} = \,\left( {5{x^2} - 1} \right)\,\,{\left( {4x + 3} \right)^,} + \,\left( {4x + 3} \right)\,{\left( {5{x^2} - 1} \right)^,} \hfill \\
Then \hfill \\
{y^,} = \left( {5{x^2} - 1} \right)\,\left( 4 \right) + \,\left( {4x + 3} \right)\,\left( {10x} \right) \hfill \\
Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\
{y^,} = 20{x^2} - 4 + 40{x^2} + 30x \hfill \\
{y^,} = 60{x^2} + 30x - 4 \hfill \\
\end{gathered} \]