TeX Quellcode:

\begin{array}{rcl}f'_{xy}(x,y) &=& \dfrac{54\cdot x\left(x+9y\right)^2-\left(6x-6x\ln(x)+54y\right)\cdot 2x\left(x+9y\right)^{2-1}\cdot 9}{x^2\left(x+9y\right)^4} \\\\&=& \dfrac{x\left(x+9y\right)\left[54\left(x+9y\right)-\left(6x-6x\ln(x)+54y\right)\cdot 18\right]}{x^2\left(x+9y\right)^4} \\\\&=& \dfrac{54x+486y-108x+108x\ln(x)-972y}{x\left(x+9y\right)^3} \\\\&=& \dfrac{-54x-486y+108x\ln(x)}{x\left(x+9y\right)^3}\end{array}