Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - 4.4 Derivatives of Exponential Functions - 4.4 Exercises: 13

Answer

\[{y^,} = x{e^x} + {e^x}\]

Work Step by Step

\[\begin{gathered} y = x{e^x} \hfill \\ Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,the\,\,derivative \hfill \\ {y^,} = \,\left( x \right)\,{\left( {{e^x}} \right)^,} + \left( {{e^x}\,} \right)\,{\left( x \right)^,} \hfill \\ Then \hfill \\ {y^,} = x\,\left( {{e^x}} \right) + {e^x}\,\left( 1 \right) \hfill \\ Multiplying\, \hfill \\ {y^,} = x{e^x} + {e^x} \hfill \\ \end{gathered} \]
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