TeX source:
\begin{array}{rcl} f'_{zy}(x,y,z) &=& \dfrac{0\cdot\left(17x^2+y^2\right)-(-16xz)\cdot 2y}{\left(17x^2+y^2\right)^2} \\\\&=& \dfrac{32xyz}{\left(17x^2+y^2\right)^2}\end{array}