TeX Quellcode:

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