- TeX source:
- \begin{array}{rcl} f'_{yy}(x,y,z) &=& \dfrac{16xz^2 \cdot\left(17x^2+y^2\right)^2-16xyz^2\cdot 2(17x^2+y^2)\cdot 2y}{\left(\left(17x^2+y^2\right)^2\right)^2} \\\\&=& \dfrac{\left(17x^2+y^2\right)\left[16xz^2 \cdot\left(17x^2+y^2\right)-16xyz^2\cdot 2\cdot 2y\right]}{\left(17x^2+y^2\right)^4} \\\\&=& \dfrac{16xz^2 \cdot\left(17x^2+y^2\right)-16xyz^2\cdot 2\cdot 2y}{\left(17x^2+y^2\right)^3} \\\\&=& \dfrac{272x^3z^2+16xy^2z^2-64xy^2z^2}{\left(17x^2+y^2\right)^3} \\\\&=& \dfrac{272x^3z^2-48xy^2z^2}{\left(17x^2+y^2\right)^3}\end{array}