Difference Between Differentiation on Time vs Position I'm hoping somebody could help me understand the difference between the following:
$$∂_tc(x,t)$$
$$∂_xc(x,t)$$
My understanding is the the top derivative would be something like velocity but what would that make the bottom derivative?
Thanks.

$∂_tc(x,t)$ represents the rate of change in $c$ with respect to $t$ (temperature) at a fixed $x$ (position), whereas $∂_xc(x,t)$ represents the rate of change in n $c$ with respect to $x$ (position) at a fixed $t$ (time).
Here is an example:
Consider a thin metal pipe filled with an aqueous solution being heated at only one end. Let $C(x, \, y)$ denote the concentration of a reactive solute $x$ meters from the beginning of the pipe at time $t$.
Here, $∂_tC(x,t)$ represents the rate of change of concentration of the solute at a specific fixed position from the beginning of the pipe, at any time $t$.
On the other hand, $∂_xC(x,t)$ represents the rate of change of concentration of the  solute at a specific fixed time at any position $x$.
Does this help?
