#### Answer

\[\frac{{dy}}{{dx}} = 4{e^{4x}}\]

#### Work Step by Step

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