Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 223: 17


$T'(z)=\frac{2^{z}}{z \ln 2}+2^{z} \ln z$

Work Step by Step

$T(z)=2^{z} \log _{2} z\\ T'(z)=\left(2^{z}\right)\left(\frac{1}{z \ln 2}\right)+\left(2^{z} \ln 2\right)\left(\log _{2} z\right)\\ T'(z)=\frac{2^{z}}{z \ln 2}+\frac{\left(2^{z} \ln 2\right)(\ln z)}{(\ln 2)}\\ T'(z)=\frac{2^{z}}{z \ln 2}+2^{z} \ln z$
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