#### Answer

\[\frac{{dr}}{{d\theta }} = 2{e^{2\theta }}\,\]

#### Work Step by Step

\[\begin{gathered}
r = {e^{2\theta }} \hfill \\
\hfill \\
Use\,\,the\,\,formula\,\,\,\frac{d}{{dx}}\,\left( {{e^u}} \right) = {e^u} \cdot {u^,}\, \hfill \\
\hfill \\
Therefore \hfill \\
\hfill \\
\frac{{dr}}{{d\theta }} = {e^{2\theta }}\,{\left( {2\theta } \right)^,} \hfill \\
\hfill \\
differentiate \hfill \\
\hfill \\
\frac{{dr}}{{d\theta }} = {e^{2\theta }}\,\left( 2 \right) \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
\frac{{dr}}{{d\theta }} = 2{e^{2\theta }}\, \hfill \\
\end{gathered} \]