Vector function derivative

Question

If a function $f(t,x)$ has $x \in \mathbb{R}^{2}$, what is the partial derivative $\frac{\partial{f}}{\partial{x}}$? Thank you greatly.

Answer 1

In such context, $\partial f/\partial x$ can simply denote $(\partial f/\partial x_1, \partial f/\partial x_2)$, where $x=(x_1,x_2)$. Probably this is the most common meaning of it.