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