TeX Quellcode:

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