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: 58


$f'(t)=(\frac{1}{2ln2})(\frac{3 (\sqrt t) ln(t+1)}{2}+\frac{t \sqrt t}{t+1})$

Work Step by Step

$f(t)=t^{\frac{3}{2}} \frac{ln(t+1)^{\frac{1}{2}}}{ln2}$ $=\frac{t^{\frac{3}{2}}(\frac{1}{2})ln(t+1)}{ln2}$ $f(t)=\frac{1}{2ln2}(t^{\frac{3}{2}})ln(t+1)$ let $u=t^{\frac{3}{2}}$ $u'=\frac{3t^{\frac{1}{2}}}{2}$ $v=ln(t+1)$ $v'=\frac{1}{t+1}$ $f'(t)=(\frac{1}{2ln2})(\frac{3 (\sqrt t) ln(t+1)}{2}+\frac{t \sqrt t}{t+1})$
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