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: 12

Answer

\[\,\left( { - \infty ,0} \right) \cup \,\left( {0,\infty } \right)\]

Work Step by Step

\[\begin{gathered} \frac{d}{{dx}}\,\left( {\ln 2{x^8}} \right) \hfill \\ \hfill \\ Use\,\,\,the\,\,formula\,\,\frac{d}{{dx}}\,\,\left[ {\ln u} \right] = \frac{{{u^,}}}{u} \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \frac{d}{{dx}}\,\left( {\ln 2{x^8}} \right) = \frac{{\frac{d}{{dx}}\left[ {\ln 2{x^8}} \right]}}{{2{x^8}}} \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \frac{{16{x^7}}}{{2{x^8}}} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{8}{{{x}}} \hfill \\ \hfill \\ Interval \hfill \\ \hfill \\ \,\left( { - \infty ,0} \right) \cup \,\left( {0,\infty } \right) \hfill \\ \end{gathered} \]
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