Answer
\[{y^,} = - 24{e^{3x}}\]
Work Step by Step
\[\begin{gathered}
y = - 8{e^{3x}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = \,{\left( { - 8{e^{3x}}} \right)^,} \hfill \\
{y^,} = - 8\,{\left( {{e^{3x}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{y^,} = - 8\,\left( {{e^{3x}}} \right)\,{\left( {3x} \right)^,} \hfill \\
{y^,} = - 8\,\left( {{e^{3x}}} \right)\,\left( 3 \right) \hfill \\
{y^,} = - 24{e^{3x}} \hfill \\
\end{gathered} \]