Differentiation — Maths STD 12 Science — Question

Let $u=3^x$
$\frac{ du }{d x}=3^x \log 3$
Let $v=\log _3 x=\frac{\log x}{\log 3}$
$\frac{ dv }{d x}=\frac{1}{\log 3} \frac{d}{d x}(\log x)$
$=\frac{1}{\log 3} \frac{1}{x}=\frac{1}{x \log 3}$
$\frac{ du }{ dv }=\frac{\frac{ du }{d x}}{\frac{ dv }{d x}}=\frac{3^x \log 3}{\frac{1}{x \log 3}}=3^x \cdot x(\log 3)^{\wedge} 2$