TeX source:
\begin{array}{rcl} f'_x(x,y,z) &=& \dfrac{-8z^2\cdot (17x^2+y^2) - \left(-8xz^2\right) \cdot 34x}{\left(17x^2+y^2\right)^2} \\\\ &=& \dfrac{-136x^2z^2-8y^2z^2+272x^2z^2}{\left(17x^2+y^2\right)^2} \\\\&=& \dfrac{136x^2z^2-8y^2z^2}{\left(17x^2+y^2\right)^2} \end{array}