Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 362: 45


$h'(x)=-\frac{(\ln 2)(cos (\pi θ))+(\pi)(sin (\pi θ))}{2^θ}$

Work Step by Step

$h(θ)=2^{-θ}cos(\pi θ)$ $u=2^{-θ}$ $u’=-\ln 2 (2^{-θ})$ $v=cos (\pi θ)$ $v’=-\pi sin (\pi θ)$ $h’(x)=u’v+uv’$ $=(-\ln 2)(2^{-θ})(cos (\pi θ))+(2^{-θ})(-\pi)(sin (\pi θ))$ $=-\frac{(\ln 2)(cos (\pi θ))+(\pi)(sin (\pi θ))}{2^θ}$
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