Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - 4.2 Derivatives of Products and Quotients - 4.2 Exercises: 9

Answer

\[{p^,}\,\left( y \right) = \, - 8{y^{ - 5}} + 15{y^{ - 6}} + 30{y^{ - 7}}\]

Work Step by Step

\[\begin{gathered} p\,\left( y \right) = \,\left( {{y^{ - 1}} + {y^{ - 2}}} \right)\,\left( {2{y^{ - 3}} - 5{y^{ - 4}}} \right) \hfill \\ Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{p^,}\,\left( y \right) \hfill \\ {p^,}\,\left( y \right) = \,\left( {{y^{ - 1}} + {y^{ - 2}}} \right)\,{\left( {2{y^{ - 3}} - 5{y^{ - 4}}} \right)^,} + \,\left( {2{y^{ - 3}} - 5{y^{ - 4}}} \right)\,{\left( {{y^{ - 1}} + {y^{ - 2}}} \right)^,} \hfill \\ Then \hfill \\ {p^,}\,\left( y \right) = \,\left( {{y^{ - 1}} + {y^{ - 2}}} \right)\,\left( { - 6{y^{ - 4}} + 20{y^{ - 5}}} \right) + \,\left( {2{y^{ - 3}} - 5{y^{ - 4}}} \right)\,\left( { - {y^{ - 1}} - 2{y^{ - 3}}} \right) \hfill \\ Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\ {p^,}\,\left( y \right) = \, - 6{y^{ - 5}} + 20{y^{ - 6}} - 6{y^{ - 6}} + 20{y^{ - 7}} - 2{y^{ - 5}} - 4{y^{ - 6}} + 5{y^{ - 6}} + 10{y^{ - 7}} \hfill \\ {p^,}\,\left( y \right) = \, - 8{y^{ - 5}} + 15{y^{ - 6}} + 30{y^{ - 7}} \hfill \\ \end{gathered} \]
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.