TeX source:
\begin{array}{rcl}f'_x(x,y) &=& \dfrac{6\cdot\dfrac{1}{x}\cdot\left(x+9y\right)-6\ln(x)\cdot 1}{\left(x+9y\right)^2} \\\\&=&\dfrac{6\left(x+9y\right)-6x\ln(x)}{x\left(x+9y\right)^2} \\\\&=& \dfrac{6x-6x\ln(x)+54y}{x(x+9y)^2}\end{array}