TeX source:
\begin{array}{rcl} f'_y(x,y,z) &=& \dfrac{0 \cdot \left(17x^2 + y^2\right) - \left(-8xz^2\right) \cdot 2y}{\left(17x^2+y^2\right)^2} \cr \cr &=& \dfrac{16xyz^2}{\left(17x^2+y^2\right)^2}\end{array}