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