Calculus: Early Transcendentals (2nd Edition)

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

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises: 35

Answer

\[ = {e^{5x}}\csc x\,\left( {5 - \cot x} \right)\]

Work Step by Step

\[\begin{gathered} y = {e^{5x}}\csc x \hfill \\ \hfill \\ Using\,\,product\,\,rule \hfill \\ \hfill \\ y' = \,{\left( {{e^{5x}}} \right)^\prime } \cdot \csc x + {e^{5x}} \cdot \,{\left( {\csc x} \right)^\prime } \hfill \\ \hfill \\ then \hfill \\ \hfill \\ = 5{e^{5x}}\csc x + {e^{5x}} \cdot \,\left( { - \csc x\,\cot x} \right) \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ = 5{e^{5x}}\csc x - {e^{5x}}\csc x\cot x \hfill \\ \hfill \\ factor \hfill \\ \hfill \\ = {e^{5x}}\csc x\,\left( {5 - \cot x} \right) \hfill \\ \end{gathered} \]
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.