TeX source:
\begin{array}{rcl}f'_{zy}(x,y,z) &=& \dfrac{9}{2}\cdot\dfrac{1}{2}x^2y^{\frac{1}{2}-1}z^2\\\\&=& \dfrac{9}{4}x^2y^{-\frac{1}{2}}z^2\end{array}