Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 23


$$ f'(x)= \frac{ e^x-4}{e^x-4x}.$$

Work Step by Step

Recall that $(\ln x)'=\dfrac{1}{x}$ Recall that $(e^x)'=e^x$ Since $ f(x)= \ln(e^x-4x)$, then the derivative, using the chain rule, is given by $$ f'(x)= \frac{ 1}{e^x-4x}(e^x-4x)'= \frac{ e^x-4}{e^x-4x}.$$
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