Writing a partial derivative as a function of time

Question

I have two time-dependent variables $x$ and $y$. Now I want to write $\dfrac{\partial x}{\partial y}$ at particular time step ($t$).

What is the correct format to write such expression?

$\dfrac{\partial x(t)}{\partial y(t)}$ or $\dfrac{\partial x}{\partial y}(t)$ is correct or both?

Answer 1

This isn't totally standardised, but I like this notation: $$ \frac{\partial x}{\partial y} {\Big\rvert}_t $$

Answer 2

We usually write

$$\left(\dfrac{\partial x}{\partial y}\right)_{t}$$

to express the fact that $t$ is hold constant.