Ah, language. It's so hard to get yourself understood if you don't use the correct terms...
The gradient function does not return functions. Not one, not multiple. It returns numerical matrices / vectors. It will return as many outputs as you have requested, so if you ask for multiple output, you'll get multiple outputs. If you ask for one, you'll only get one. Each output is the gradient of the input matrix along the corresponding dimension. I have no idea what you mean by 'root'
I also have no idea what this X you want to substitute is. You get the gradient at each point in your original matrix. If you want the gradient at points in between you either interpolate your input, or interpolate your output.
Finally, what is a slope field. quiver just plots arrow in the direction you specify. If it's the gradient of you matrix you want to plot with quiver, just pass the output of gradient to quiver (as per the example in the doc of gradient).
