Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises: 77

Answer

\[{f^,}\,\left( x \right) = \frac{{12}}{{3x + 1}}\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = \ln \,{\left( {3x + 1} \right)^4} \hfill \\ \hfill \\ Use\,\,\ln {a^u} = u\ln a \hfill \\ \hfill \\ f\,\left( x \right) = 4\ln \,\left( {3x + 1} \right) \hfill \\ \hfill \\ Differentiate{\text{ }}Use\,\,\frac{d}{{dx}}\,\,\left[ {\ln u} \right] = \frac{{{u^,}}}{u} \hfill \\ \hfill \\ {f^,}\,\left( x \right) = 4\,\left( {\frac{3}{{3x + 1}}} \right) \hfill \\ \hfill \\ Simplify \hfill \\ \hfill \\ {f^,}\,\left( x \right) = \frac{{12}}{{3x + 1}} \hfill \\ \end{gathered} \]
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