Prerequisite concepts
The derivative is a function
One of Zandieh's process-object layers for derivatives is that derivatives are functions. This means that the value of a derivative depends on where in the domain of the function one is looking. The derivative of a function is itself a function, with the same domain as the original function. Both the (derivative) function and the value of the derivative at a point are commonly referred to as "the derivative."
The partial derivative of a function is itself a function (although taking a partial derivative at a point will just give a number). This means that the value of the partial derivative at different points in the domain will, in general, be different.
The gradient of a function (unless taken at a single point) is itself a function
The divergence of a function (unless taken at a single point) is itself a function
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