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: 25

Answer

\[{y^,} = 3\ln 7\,\left( {{7^{3x + 1}}} \right)\]

Work Step by Step

\[\begin{gathered} y = {7^{3x + 1}} \hfill \\ Find\,\,the\,\,derivative \hfill \\ {y^,} = \,{\left( {{7^{3x + 1}}} \right)^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Then \hfill \\ Let\,\,a = 7\,,\,g\,\left( x \right) = 3x + 1 \hfill \\ {y^,} = \,\left( {\ln 7} \right){7^{3x + 1}}\,{\left( {3x + 1} \right)^,} \hfill \\ {y^,} = 3\ln 7\,\left( {{7^{3x + 1}}} \right) \hfill \\ \hfill \\ \end{gathered} \]
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