## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter 4 - Calculating the Derivative - 4.4 Derivatives of Exponential Functions - 4.4 Exercises - Page 232: 9

#### Answer

${y^,} = 12x{e^{2{x^2}}}$

#### Work Step by Step

$\begin{gathered} y = 3{e^{2{x^2}}} \hfill \\ Find\,\,the\,\,derivative \hfill \\ {y^,} = \,{\left( {3{e^{2{x^2}}}} \right)^,} \hfill \\ {y^,} = 3\,{\left( {{e^{2{x^2}}}} \right)^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{e^{g\,\left( x \right)}}} \right] = {e^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Then \hfill \\ {y^,} = 3\,\left( {{e^{2{x^2}}}} \right)\,{\left( {2{x^2}} \right)^,} \hfill \\ {y^,} = 3\,\left( {{e^{2{x^2}}}} \right)\,\left( 4 \right) \hfill \\ Multiplying\, \hfill \\ {y^,} = 12x{e^{2{x^2}}} \hfill \\ \hfill \\ \end{gathered}$

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