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