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: 2

Answer

\[\frac{{dy}}{{dx}} = - 2{e^{ - 2x}}\]

Work Step by Step

\[\begin{gathered} y = {e^{ - 2x}} \hfill \\ Find\,\,the\,\,derivative\,\,using\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\left( {{e^{g\,\left( x \right)}}} \right) = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Then \hfill \\ \frac{{dy}}{{dx}} = {e^{ - 2x}}\,{\left( { - 2x} \right)^,} \hfill \\ \frac{{dy}}{{dx}} = {e^{ - 2x}}\,\left( { - 2} \right) \hfill \\ Multiplying\, \hfill \\ \frac{{dy}}{{dx}} = - 2{e^{ - 2x}} \hfill \\ \end{gathered} \]
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