Calculus: Early Transcendentals (2nd Edition)

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

Chapter 3 - Derivatives - 3.8 Implicit Differentiation - 3.8 Exercises: 39

Answer

\[\frac{{dy}}{{dx}} = \frac{{10}}{{3\sqrt[3]{{5x + 1}}}}\]

Work Step by Step

\[\begin{gathered} y = \,{\left( {5x + 1} \right)^{\frac{2}{3}}} \hfill \\ \hfill \\ differentiate \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{2}{3}\,{\left( {5x + 1} \right)^{\frac{2}{3} - 1}}\,\left( 5 \right) \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{{10}}{{3\,{{\left( {5x + 1} \right)}^{\frac{1}{3}}}}} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{{10}}{{3\sqrt[3]{{5x + 1}}}} \hfill \\ \end{gathered} \]
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.