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: 16

Answer

\[{F^,}\,\left( x \right) = - 19{x^{ - 2}} - 4{x^{ - 1/2}}\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 19{x^{ - 1}} - 8\sqrt x \hfill \\ Write\,\sqrt x \,\,as\,\,{x^{1/2}} \hfill \\ Find\,\,the\,\,derivative\, \hfill \\ {F^,}\,\left( x \right) = 19{x^{ - 1}} - 8{x^{1/2}} \hfill \\ find\,\,the\,\,derivative\, \hfill \\ {F^,}\,\left( x \right) = \frac{d}{{dx}}\,\,\left[ {19{x^{ - 1}} - 8{x^{1/2}}} \right] \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\ Then \hfill \\ {F^,}\,\left( x \right) = 19\,\left( { - 1} \right){x^{ - 1 - 1}} - 8\,\left( {\frac{1}{2}} \right){x^{1/2 - 1}} \hfill \\ {F^,}\,\left( x \right) = - 19{x^{ - 2}} - 4{x^{ - 1/2}} \hfill \\ \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.