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: 25

Answer

\[\frac{{dy}}{{dx}} = 5\ln 4 \cdot {4^x}\]

Work Step by Step

\[\begin{gathered} y = 5 \cdot {4^x} \hfill \\ \hfill \\ Use\,\,the\,formula\,\,\frac{d}{{dx}}\,\,\left[ {{a^u}} \right] = {a^u}\ln a \cdot {u^,} \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = 5\,\left( {{4^x}\ln 4 \cdot 1} \right) \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = 5\ln 4 \cdot {4^x} \hfill \\ \end{gathered} \]
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