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: 1

Answer

\[{y^,} = 18{x^2} - 6x + 4\]

Work Step by Step

\[\begin{gathered} y = \,\left( {3{x^2} + 2} \right)\,\left( {2x - 1} \right) \hfill \\ Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{y^,} \hfill \\ {y^,} = \,{\left( {3{x^2} + 2} \right)^,}\,\left( {2x - 1} \right) + \,{\left( {2x - 1} \right)^,}\,\left( {3{x^2}2} \right) \hfill \\ Then \hfill \\ {y^,} = \,\left( {6x} \right)\,\left( {2x - 1} \right) + \,\left( 2 \right)\,\left( {3{x^2} + 2} \right) \hfill \\ Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\ {y^,} = 12{x^2} - 6x + 6{x^2} + 4 \hfill \\ {y^,} = 18{x^2} - 6x + 4 \hfill \\ \hfill \\ \end{gathered} \]
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