Answer
$=\frac{1}{\ln 3}(\frac{3x-2}{2x(x-1)})$
Work Step by Step
$h(x)=\frac{\ln\left(\frac{x(x-1)^{\frac{1}{2}}}{2}\right)}{\ln 3}$
$=\frac{\ln x+ \frac{1}{2} \ln(x-1) - \ln 2}{\ln 3}$
$h’(x)= \frac{1}{\ln 3}(\frac{1}{x}+\frac{1}{2x-2}-0)$
$=\frac{1}{\ln 3}(\frac{3x-2}{2x(x-1)})$
