Calculus with Applications (10th Edition)

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

Chapter 4 - Calculating the Derivative - 4.5 Derivatives of Logarithmic Functions - 4.5 Exercises: 24

Answer

\[{y^,} = \frac{{\ln 4}}{x}\]

Work Step by Step

\[\begin{gathered} y = \,\left( {\ln 4} \right)\,\left( {\ln \left| {3x} \right|} \right) \hfill \\ Differentiate \hfill \\ {y^,} = \,\,{\left[ {\,\left( {\ln 4} \right)\,\left( {\ln \left| {3x} \right|} \right)} \right]^,} \hfill \\ Pull\,\,out\,\,the\,\,constant \hfill \\ {y^,} = \ln 4\,\,{\left[ {\ln \left| {3x} \right|} \right]^,} \hfill \\ Use\,\,the\,\,\,formula \hfill \\ \frac{d}{{dx}}\,\,\left[ {\ln g\,\left( x \right)} \right] = \frac{{{g^,}\,\left( x \right)}}{{g\,\left( x \right)}} \hfill \\ Then \hfill \\ {y^,} = \ln 4\,\left( {\frac{{\,{{\left( {3x} \right)}^,}}}{{3x}}} \right) \hfill \\ {y^,} = \ln 4\,\left( {\frac{3}{{3x}}} \right) \hfill \\ {y^,} = \frac{{\ln 4}}{x} \hfill \\ \hfill \\ \end{gathered} \]
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