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: 37

Answer

\[\frac{{dy}}{{dx}} = \frac{{5\sqrt[4]{x}}}{4}\]

Work Step by Step

\[\begin{gathered} y = {x^{\frac{5}{4}}} \hfill \\ \hfill \\ use\,\,the\,\,Implicit\,\,differentiation \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{5}{4}{x^{\frac{5}{4} - 1}} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{5}{4}{x^{\frac{1}{4}}} \hfill \\ \hfill \\ {x^{1/4}} = \sqrt[4]{x}\,\,then \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{{5\sqrt[4]{x}}}{4} \hfill \\ \end{gathered} \]
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