TeX Quellcode:

\begin{array}{rcl}f'_{xx}(x,y) &=& \dfrac{\left(6-6\ln(x)-6x\cdot\frac{1}{x}\right)\cdot x\left(x+9y\right)^2-\left(6x-6x\ln(x)+54y\right)\cdot\left(1\cdot\left(x+9y\right)^2+x\cdot 2\left(x+9y\right)\cdot 1\right)}{x^2\left(x+9y\right)^4} \\\\&=& \dfrac{\left(6-6\ln(x)-6\right)\cdot x\left(x+9y\right)^2-\left(6x-6x\ln(x)+54y\right)\cdot\left(\left(x+9y\right)^2+2x(x+9y)\right)}{x^2\left(x+9y\right)^4} \\\\&=& \dfrac{(x+9y)\left[-6\ln(x)\cdot x\left(x+9y\right)-\left(6x-6x\ln(x)+54y\right)\cdot\left(\left(x+9y\right)+2x\right)\right]}{x^2\left(x+9y\right)^4} \\\\&=& \dfrac{-6x\ln(x)\cdot\left(x+9y\right)-\left(6x-6x\ln(x)+54y\right)\cdot\left(3x+9y\right)}{x^2\left(x+9y\right)^3} \\\\&=& \dfrac{-6x^2\ln(x)-54xy\ln(x)-18x^2+18x^2\ln(x)-162xy-54xy+54xy\ln(x)-486y^2}{x^2\left(x+9y\right)^3} \\\\&=& \dfrac{12x^2\ln(x)-18x^2-216xy-486y^2}{x^2\left(x+9y\right)^3}\end{array}