When writing out Nabla as a "vector of derivatives," are the elements in that vector acting more like operators and don't actually have a defined function until it gets applied to X?

yingsi

Is it correct to understand divergence as the total rate of change of a vector field at different locations in the space/plane?

When writing out Nabla as a "vector of derivatives," are the elements in that vector acting more like operators and don't actually have a defined function until it gets applied to X?

Is it correct to understand divergence as the total rate of change of a vector field at different locations in the space/plane?