TeX Quellcode:

\begin{array}{rcl} f'_{yy}(x,y,z) &=& \left(-6x^2y+2x\right) e^{-3xy}\ln(z) + \left(-3x^2y^2+2xy\right) e^{-3xy} \cdot (-3x) \ln(z) \\\\&=& \left(-6x^2y+2x\right) e^{-3xy}\ln(z) - 3x\left(-3x^2y^2+2xy\right) e^{-3xy} \ln(z) \\\\&=& \left[\left(-6x^2y+2x\right) - 3x\left(-3x^2y^2+2xy\right)\right] e^{-3xy} \ln(z) \\\\&=& \left[-6x^2y+2x+9x^3y^2-6x^2y\right] e^{-3xy} \ln(z) \\\\&=& \left[9x^3y^2-12x^2y+2x\right] e^{-3xy} \ln(z)\end{array}