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: 14

Answer

\[{y^,} = 12{x^{ - 4}}\]

Work Step by Step

\[\begin{gathered} y = - 4{x^{ - 3}} \hfill \\ Find\,\,the\,\,derivative\, \hfill \\ {y^,} = \frac{d}{{dx}}\,\,\left[ { - 4{x^{ - 3}}} \right] \hfill \\ {y^,} = - 4\frac{d}{{dx}}\,\,\left[ {{x^{ - 3}}} \right] \hfill \\ Use\,\,the\,\,formula \hfill \\ \,\,\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ Then \hfill \\ {y^,} = - 4\,\left( { - 3} \right){x^{ - 3 - 1}} \hfill \\ Simplifying \hfill \\ {y^,} = 12{x^{ - 4}} \hfill \\ \end{gathered} \]
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