## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 3 - Review - Exercises: 21

#### Answer

$y'=(3^{xln(x)})(ln(3))(1+ln(x))$

#### Work Step by Step

Start with the function $y=3^{xln(x)}$. Apply exponential rule to differentiate: $y'=(3^{xln(x)})ln(3)(\frac{d}{dx}(x(ln(x))))$. Use product rule to differentiate $xln(x)$: $y'=(3^{xln(x)})(ln(3))(\frac{x}{x}+1*ln(x))$. Simplify to arrive at the final answer: $y'=(3^{xln(x)})(ln(3))(1+ln(x))$.

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