Is $\frac{\mathrm d}{\mathrm dx}$ an operation? What exactly is an operation? I understand that multiplication and addition are operations, but what about the derivative ($\frac{\mathrm d}{\mathrm dx}$).
Can an operation be a relation of expressions, or just of numbers?

$\frac{d}{dx}$ is a linear operator.
And expanding on the comment made by Jack Crawford, a linear operator has a matrix representation the image of which is completely dependent on the choice of basic set of the finite vector space on which it is acting on.
