#### Answer

\[{y^,} = 16x{e^{2{x^2} - 4}}\]

#### Work Step by Step

\[\begin{gathered}
y = 4{e^{2{x^2} - 4}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,{\left( {4{e^{2{x^2} - 4}}} \right)^,} \hfill \\
{y^,} = 4\,{\left( {{e^{2{x^2} - 4}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{y^,} = 4\,\left( {{e^{2{x^2} - 4}}} \right)\,{\left( {2{x^2} - 4} \right)^,} \hfill \\
{y^,} = 4\,\left( {{e^{2{x^2} - 4}}} \right)\,\left( {4x} \right) \hfill \\
Multiplying\, \hfill \\
{y^,} = 16x{e^{2{x^2} - 4}} \hfill \\
\end{gathered} \]