Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises: 38

Answer

\[{y^,} = \frac{5}{{5x + 3}}\]

Work Step by Step

\[\begin{gathered} y = \ln \,\left( {5x + 3} \right) \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,\,function \hfill \\ {y^,} = \,\,{\left[ {\ln \,\left( {5x + 3} \right)} \right]^,} \hfill \\ Use\,\,the\,\,formula\,\,\,\,{\left[ {\ln g\,\left( x \right)} \right]^,} = \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\ {y^,} = \frac{{\,{{\left( {5x + 3} \right)}^,}}}{{5x + 3}} \hfill \\ Then \hfill \\ {y^,} = \frac{5}{{5x + 3}} \hfill \\ \end{gathered} \]
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