When a differential operator acts on a constant does this equal 0 or just the constant? For example
$ F_x a $
Where Fx is the first order difference operator and a is constant
The concept of a Derivative means the limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero.
A constant remains constant irrespective of any change to any variable in the function therefore, its derivative is $0$.