Calculus 8th Edition

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

Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 33


$$y' =3 ^{x \ln x}(\ln 3)[1+\ln x]$$

Work Step by Step

Given $$ y=3 ^{x \ln x}$$ Then \begin{align*} y'&=3 ^{x \ln x}(\ln 3)\frac{d}{dx}(x \ln x)\\ &=3 ^{x \ln x}(\ln 3)[x\frac{1}{x}+\ln x]\\ &=3 ^{x \ln x}(\ln 3)[1+\ln x] \end{align*}
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