TeX source:
\begin{array}{rcl}g'_x(x,y) &=& 52e^y+\dfrac{y}{8}\cdot\dfrac{1}{x}\\\\&=& 52e^y+\dfrac{y}{8x}\\\\&=& 52e^y+\dfrac{1}{8}x^{-1}y\end{array}