Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 30


$$y'=\frac{\ln \left(t^4\right)+4}{2\sqrt{t\ln \left(t^4\right)}}$$

Work Step by Step

Given $$y=\sqrt{t\ln t^4}$$ Then \begin{align*} y'&=\frac{1}{2\sqrt{t\ln \left(t^4\right)}}\left(\frac{d}{dt}\left(t\right)\ln \left(t^4\right)+\frac{d}{dt}\left(\ln \left(t^4\right)\right)t\right)\\ &=\frac{\ln \left(t^4\right)+4}{2\sqrt{t\ln \left(t^4\right)}} \end{align*}
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