The 2-dimensional [[Cumulative Density Function]] is a double integral from $[-\infty,x]$ and $[-\infty,y]$ over the [[Joint Probability Density Function]] $f_{X,Y}(x,y)$. Conversely the PDF can be obtained by taking the derivative of $dx,dy$ from the CDF. $ \begin{align} \mathbf P(X \le x, Y\le y)=F_{X,Y}(x,y)&= \int_{-\infty}^y \Big (\int_{-\infty}^x f_{X,Y}(x,y) * dx \Big )* dy \\[8pt] \frac{\partial F_{X,Y}}{\partial y}(x,y)&= \int_{-\infty}^x f_{X,Y}(x,y) * dx \\[8pt] \frac{\partial^2F_{X,Y}}{\partial y\partial x}(x,y)&= f_{X,Y}(x,y) \end{align} $