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: 56

Answer

\[\frac{{dy}}{{dx}} = \frac{1}{{x\ln 10}}\]

Work Step by Step

\[\begin{gathered} y = {\log _{10}}x \hfill \\ \hfill \\ Differentiate,{\text{ use }}\frac{d}{{dx}}\left[ {{{\log }_a}u} \right] = \frac{1}{{\ln a\left( u \right)}}{u^,} \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{1}{{\,\left( {\ln 10} \right)\,\left( x \right)}}\,\left( {{x^,}} \right) \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \frac{1}{{x\ln 10}} \hfill \\ \hfill \\ \end{gathered} \]
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