I want to know if it is possible to create a variable that is an operator. (Please note I only started programming Mathematica today) For example, the partial operator $ \partial_x$ i.e.
partX = D[#,x]&
Ideally I would want to use it in the following way.
partX*(x^2)
Which would return 2x. This is mostly so I can store it and manipulate it and use it when I want to.
On a related note, I was wondering if I could do this with lists as well.
del = {D[#,x]&, D[#,y]&, D[#,z]&} del*(xyz)
Which would ideally return
{yz,xz,xy}
I was wondering how this would work because I was also hoping to create operators like $ \partial_x\partial_y$ by multiplying the variables for each individually i.e.
partXY = D[#,x]&*D[#,y]&
or
partX = D[#,x]& partY = D[#,y]& partXY = partX*partY
Please let me know if you can answer any or all of these questions. Thanks!