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: 2

Answer

\[{y^,} = 60{x^2} + 30x - 4\]

Work Step by Step

\[\begin{gathered} y = \,\left( {5{x^2} - 1} \right)\,\left( {4x + 3} \right) \hfill \\ Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{y^,} \hfill \\ {y^,} = \,\left( {5{x^2} - 1} \right)\,\,{\left( {4x + 3} \right)^,} + \,\left( {4x + 3} \right)\,{\left( {5{x^2} - 1} \right)^,} \hfill \\ Then \hfill \\ {y^,} = \left( {5{x^2} - 1} \right)\,\left( 4 \right) + \,\left( {4x + 3} \right)\,\left( {10x} \right) \hfill \\ Simplify\,\,by\,\,multiplying\,\,and\,\,combining\,\,terms \hfill \\ {y^,} = 20{x^2} - 4 + 40{x^2} + 30x \hfill \\ {y^,} = 60{x^2} + 30x - 4 \hfill \\ \end{gathered} \]
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