Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 45


$11^{x}\cdot\ln 11$

Work Step by Step

Let $y= 11^{x}$. Then, $\ln y= x \cdot \ln 11$ Differentiating both sides with respect to x, We have $\frac{1}{y}\frac{dy}{dx}=\ln 11$ Or $\frac{dy}{dx}=y\cdot \ln 11$ Thus $\frac{d}{dx}(11^{x})= 11^{x}\cdot\ln 11$
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