TeX source:
\begin{array}{rcl} f'_{xy}(x,y,z) &=& \dfrac{\left(\pi-10\pi xz\right) \cos\left(7y^5\right)\cdot 35y^4}{e^{10xz+1}} \\\\&=& \dfrac{\left(35\pi y^4-350\pi xy^4z\right) \cos\left(7y^5\right)}{e^{10xz+1}}\end{array}