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: 6

Answer

\[{g^,}\,\left( t \right) = 36{t^3} + 24t\]

Work Step by Step

\[\begin{gathered} g\,\left( t \right) = \,{\left( {3{t^2} + 2} \right)^2} \hfill \\ Write\,\,as\,a\,\,product\,\, \hfill \\ g\,\left( t \right) = \left( {3{t^2} + 2} \right)\left( {3{t^2} + 2} \right) \hfill \\ Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{g^,}\,\left( t \right) \hfill \\ {g^,}\,\left( t \right) = \,\left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} + \left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} \hfill \\ {g^,}\,\left( t \right) = 2\left( {3{t^2} + 2} \right){\left( {3{t^2} + 2} \right)^,} \hfill \\ Then \hfill \\ {g^,}\,\left( t \right) = 2\left( {3{t^2} + 2} \right)\,\left( {6t} \right) \hfill \\ Multiplying \hfill \\ {g^,}\,\left( t \right) = 12t\left( {3{t^2} + 2} \right) \hfill \\ {g^,}\,\left( t \right) = 36{t^3} + 24t \hfill \\ \end{gathered} \]
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