TeX Quellcode:

\begin{array}{rcl} f'_{xx}(x,y,z) &=& \dfrac{-10\pi z\sin\left(7y^5\right)\cdot e^{10xz+1} - \left(\pi-10 \pi xz\right)\sin\left(7y^5\right)\cdot e^{10xz+1}\cdot 10z}{\left(e^{10xz+1}\right)^2} \\\\ &=& \dfrac{\left[-10\pi z-\left(\pi-10 \pi xz\right)\cdot 10z\right]\sin\left(7y^5\right)\cdot e^{10xz+1}}{\left(e^{10xz+1}\right)^2} \\\\ &=& \dfrac{\left[-10\pi z-10\pi z+100\pi xz^2\right]\sin\left(7y^5\right)}{e^{10xz+1}} \\\\&=& \dfrac{\left[-20\pi z+100\pi xz^2\right]\sin\left(7y^5\right)}{e^{10xz+1}}\end{array}