Answer
$$y' =3 ^{x \ln x}(\ln 3)[1+\ln x]$$
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*}
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 33
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