It is general knowledge, that when we deal with derivatives of function in Mma we have to inevitably indicate variables of such functions. Namely, this
is correct, while this
is not, returning zero.
However, as soon as one has a differential expression, especially one containing multiple partial derivatives one faces a too lengthy-expression. It is often difficult to look at, leave alone to work with.
As a workaround, I imagine that it would be very helpful if one could define a function with virtual variables. Namely, I dream about a possibility to define a variable, say,
f depending on coordinates
f[x,y,z] such that the part
[x,y,z] would be invisible, though Mma is aware of its existance and treat it as if it is written down with the coordinates. In this case,
instead of zero.
If such a definition of virtual variables is possible, the advantage would be in a dramatic shortening of expressions containing differential operations.