Embed Grad, Div & Curl directly into VectorPlot3D

Questions
,
1

Hi,
Is it possible to directly embed functions such as (Grad, Div & Curl) directly into plot commands?

For example:

VectorPlot3D[
 Grad[{E^x Cos[y], E^x Sin[y], z}, {x, y, z}], {x, 0, 3}, {y, 0, 
  3}, {z, 0, 3}]

Thanks,

Mitch Sandlin

2

  1. grad is an operation , that works on a scalar function

  2. Embedding grad in a VectorPlot3D command :

    grad[f_] := {D[f, x], D[f, y], D[f, z]}
    VectorPlot3D[
    Evaluate[grad[x + y^3 Cos - Sin[z]]], {x, 0, 3}, {y, 0, 3}, {z, 0, 3}]

  3. that should work with curl as well

  4. div is a scalar, that should be plotted in another way

    div[a_] := D[a, x] + D[a, y] + D[a, z]
    ContourPlot3D[
    Evaluate[div[{x^2, Sin[x y], Exp[- x y z]}]], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]