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: 43

Answer

\[ {s^,}\,\left( t \right) = 2\,\left( {{t^2} + {e^t}} \right)\,\left( {2t + {e^t}} \right)\]

Work Step by Step

\[\begin{gathered} s = \,{\left( {{t^2} + {e^t}} \right)^2} \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,\,function \hfill \\ {s^,} = \,\,{\left[ {\,{{\left( {{t^2} + {e^t}} \right)}^2}} \right]^,} \hfill \\ Use\,\,the\,\,general\,\,\,power\,\,rule \hfill \\ {s^,} = 2\,{\left( {{t^2} + {e^t}} \right)^{2 - 1}}\,{\left( {{t^2} + {e^t}} \right)^,} \hfill \\ Then \hfill \\ {s^,}\,\left( t \right) = 2\,\left( {{t^2} + {e^t}} \right)\,\left( {2t + {e^t}} \right) \hfill \\ \end{gathered} \]
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