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: 11

Answer

\[{y^,} = 15{x^2} - 14x - 9\]

Work Step by Step

\[\begin{gathered} y = 5{x^3} - 7{x^2} - 9x + \sqrt 5 \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,function \hfill \\ {y^,} = \frac{d}{{dx}}\,\,\left[ {5{x^3} - 7{x^2} - 9x + \sqrt 5 } \right] \hfill \\ Use\,\,the\,\,formula\,\,\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ Then \hfill \\ {y^,} = 5\,\left( 3 \right){x^{3 - 1}} - 7\,\left( 2 \right){x^{2 - 1}} - 9\,\left( 1 \right) + 0 \hfill \\ Simplifying \hfill \\ {y^,} = 15{x^2} - 14x - 9 \hfill \\ \end{gathered} \]
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