Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises: 13

Answer

\[{y^,} = 24{x^{5/3}}\]

Work Step by Step

\[\begin{gathered} y = 9{x^{8/3}} \hfill \\ Differentiate \hfill \\ {y^,} = \frac{d}{{dx}}\,\,\left[ {9{x^{8/3}}} \right] \hfill \\ {y^,} = 9\frac{d}{{dx}}\,\,\left[ {{x^{8/3}}} \right] \hfill \\ Use\,\,the\,\,formula \hfill \\ \,\,\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ Then \hfill \\ {y^,} = 9\,\left( {\frac{8}{3}} \right){x^{8/3 - 1}} \hfill \\ {y^,} = 24{x^{5/3}} \hfill \\ \hfill \\ \end{gathered} \]
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