TeX source:
\begin{array}{rcl}f'_{xy}(x,y) &=& 3\cdot e^{3xy-23}+3y\cdot e^{3xy-23}\cdot 3x+\dfrac{1}{2\sqrt{x}}\\\\&=& 3e^{3xy-23}+9yxe^{3xy-23}+\dfrac{1}{2\sqrt{x}}\end{array}