TeX source:
\begin{array}{rcl}f'_{yx}(x,y) &=& 2y\cdot (-1)\left(x+y^2\right)^{-1-1}\cdot 1\\& & -2\cdot e^{2xy}-2xe^{2xy}\cdot 2y\\\\&=& -\dfrac{2y}{\left(x+y^2\right)^2}+\left(-2-4xy\right)e^{2xy}\end{array}