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: 29

Answer

\[{s^,} = \frac{{\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)}}{{\sqrt t }}\]

Work Step by Step

\[\begin{gathered} s = 2 \cdot {3^{\sqrt t }} \hfill \\ Find\,\,the\,\,derivative \hfill \\ {s^,} = \,\,\,{\left[ {2 \cdot {3^{\sqrt t }}} \right]^,} \hfill \\ Pull\,\,out\,\,the\,\,constant\,\,2 \hfill \\ {s^,} = 2\,\,{\left[ {{3^{\sqrt t }}} \right]^,} \hfill \\ Use\,\,the\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {{a^{g\,\left( x \right)}}} \right] = \,\left( {\ln a} \right){a^{g\,\left( x \right)}}{g^,}\,\left( x \right) \hfill \\ Then \hfill \\ {s^,} = 2\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)\,{\left( {\sqrt t } \right)^,} \hfill \\ Differentiate \hfill \\ {s^,} = 2\,\left( {\ln 3} \right)\,1\left( {{3^{\sqrt t }}} \right)\,\left( {\frac{1}{{2\sqrt t }}} \right) \hfill \\ {s^,} = \frac{{\,\left( {\ln 3} \right)\,\left( {{3^{\sqrt t }}} \right)}}{{\sqrt t }} \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.