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 - Page 232: 3

Answer

\[{y^,} = - 24{e^{3x}}\]

Work Step by Step

\[\begin{gathered} y = - 8{e^{3x}} \hfill \\ Find\,\,the\,\,derivative \hfill \\ {y^,} = \,{\left( { - 8{e^{3x}}} \right)^,} \hfill \\ {y^,} = - 8\,{\left( {{e^{3x}}} \right)^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Then \hfill \\ {y^,} = - 8\,\left( {{e^{3x}}} \right)\,{\left( {3x} \right)^,} \hfill \\ {y^,} = - 8\,\left( {{e^{3x}}} \right)\,\left( 3 \right) \hfill \\ {y^,} = - 24{e^{3x}} \hfill \\ \end{gathered} \]
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