How to write the first order condition for a joint convex function $f(x,y)$, $x\in \mathbb{R}^{n}$ and $y\in \mathbb{R}^{n}$

Question

How to write the first oder condition of a convex function $f(x,y):\mathbb{R}^{n}\times\mathbb{R}^{n}\rightarrow\mathbb{R} $ where $x\in \mathbb{R}^{n}$, $y\in \mathbb{R}^{n}$ and $f(x,y)$ is joint convex in $x$ and $y$. We assume $f$ function has subgradients (or gradients if it is differentiable) in its domain.