TeX source:
\begin{array}{rcl} f'_{zy}(x,y,z) &=& -\dfrac{10\pi x^2\cos\left(7y^5\right)\cdot 35y^4}{e^{10xz+1}} \\\\&=& -\dfrac{350\pi x^2y^4\cos\left(7y^5\right)}{e^{10xz+1}}\end{array}