TeX source:
\begin{array}{rcl}g'_{xy}(x,y) &=& -\dfrac{7}{10}\sin(x)\cdot(-1)y^{-1-1}+19\\\\&=& \dfrac{7}{10}\sin(x)\cdot y^{-2}+19\\\\&=& \dfrac{7\sin(x)}{10y^2}+19\end{array}