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: 59

Answer

$\frac{dy}{dx} = \frac{-1}{x\ln(4)(\log_{4}(x))^2}$

Work Step by Step

$y = \frac{1}{\log_{4}(x)}$ Quotient Rule: $\frac{dy}{dx} = \frac{(0)(\log_{4}(x))-(1)\left(\frac{1}{x\ln(4)}\right)}{(\log_{4}(x))^2} = \frac{-1}{x\ln(4)(\log_{4}(x))^2}$
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