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 - Page 211: 19

Answer

\[ = \frac{1}{{x\ln x}}\]

Work Step by Step

\[\begin{gathered} \frac{d}{{dx}}\,\,\left[ {\ln \,\left( {\ln x} \right)} \right] \hfill \\ \hfill \\ Use\,\,\frac{d}{{dx}}\,\,\left[ {\ln u} \right] = \frac{{{u^,}}}{u} \hfill \\ \hfill \\ Set\,\,u = \ln x \hfill \\ \,\,\,\,\,\,\,\,\,\,\,{u^,} = \frac{1}{x} \hfill \\ \hfill \\ Therefore \hfill \\ \hfill \\ = \frac{{\frac{1}{x}}}{{\ln x}} \hfill \\ \hfill \\ Simplify \hfill \\ \hfill \\ = \frac{1}{{x\ln x}} \hfill \\ \end{gathered} \]
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.