>>14254166You have a function. That has multiple variables, x, y, and z.
You have input. It's one number, but it has multiple dimensions, i, j, k, like a matrix.
You create an operator that assigns partial derivatives per each function variable to each input dimension, like d/dx i, d/dy j, d/dz k. That produces a vector of it's own.
A derivative of the gradient is just that process twice.
Not asked, but the Laplace Operator results in a scalar. That gives how much the gradient field sucks or blows.
Not asked, but the curl results in a scalar. That gives how much the gradient is rubbing it around, clockwise or counter clockwise.
Higher dimension derivatives, with respect to time, represent how tethered something is. An accelerating car going over bumpy hills is four derivatives deep. Slam on the breaks, and have a neck and you are five, six, seven derivatives dependent upon ta breaking position.
