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: 15

Answer

\[{F^,}\,\left( x \right) = - 12{x^{ - 5}} + 3{x^{ - 1/2}}\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 3{x^{ - 4}} + 6\sqrt x \hfill \\ Write\,\sqrt x \,\,as\,\,{x^{1/2}} \hfill \\ Find\,\,the\,\,derivative\, \hfill \\ F\left( x \right) = \frac{d}{{dx}}\,\,\left[ {3{x^{ - 4}} + 6{x^{1/2}}} \right] \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ Then \hfill \\ {F^,}\,\left( x \right) = 3\,\left( { - 4} \right){x^{ - 4 - 1}} + 6\,\left( {\frac{1}{2}} \right){x^{1/2 - 1}} \hfill \\ {F^,}\,\left( x \right) = - 12{x^{ - 5}} + 3{x^{ - 1/2}} \hfill \\ \end{gathered} \]
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