Answer
\[{y^,} = - 18x{e^{3{x^2} + 5}}\]
Work Step by Step
\[\begin{gathered}
y = - 3{e^{3{x^2} + 5}} \hfill \\
Find\,\,the\,\,derivative \hfill \\
{y^,} = {\left( { - 3{e^{3{x^2} + 5}}} \right)^,} \hfill \\
{y^,} = - 3\,{\left( {{e^{3{x^2} + 5}}} \right)^,} \hfill \\
Use\,\,the\,\,formula \hfill \\
\frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\
Then \hfill \\
{y^,} = - 3\,\left( {{e^{3{x^2} + 5}}} \right)\,{\left( {3{x^2} + 5} \right)^,} \hfill \\
{y^,} = - 3\,\left( {{e^{3{x^2} + 5}}} \right)\,\,\left( {6x} \right) \hfill \\
Multiplying\, \hfill \\
{y^,} = - 18x{e^{3{x^2} + 5}} \hfill \\
\end{gathered} \]
