Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises: 39

Answer

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

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.