TeX source:
\begin{array}{rcl}f'_{yy}(x,y,z) &=& -\dfrac{3}{4}\cdot\dfrac{1}{2}x^2y^{-\frac{1}{2}-1}z^3+8x^{\frac{1}{3}}\\\\&=& -\dfrac{3}{8}x^2y^{-\frac{3}{2}}z^3+8x^{\frac{1}{3}}\end{array}