## Calculus: Early Transcendentals 8th Edition

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