Notebook 3

<< Calculus`VectorAnalysis`

SetCoordinates[Cartesian[x, y, z]];

lhs  =  
      Curl[f[x, y, z] {m[x, y, z],  n[x, y, z],  p[x, y, z]}]  //  
        Simplify

rhs  =  
      f[x, y, z] Curl[{m[x, y, z],  n[x, y, z],  p[x, y, z]}]  +  
        Cross[Grad[f[x, y, z]],  {m[x, y, z],  n[x, y, z],  p[x, y, z]}]

lhs  -  rhs  //  Simplify

Curl[{x, y, z}]