

Gradient operator on Nokia N810
of a (negative) eletric potential yielding the eletric vector field in
spherical coordinates.

Divergence operator on Nokia
N900 of a eletric vector field in spherical coordinate system, with the
result given in terms of Dirac delta function.

Curl of a generic function in
cartesian coordinate system on Nokia N900.

First terms of the laplacian operator of a generic function in spherical coordinate system on Nokia N900. 
Menu of "Derivative" on Nokia N900 shows that the vector differential operators (grad, div, curl and laplacian) are also available. 
The default settings of "Derivative" on Nokia N900. Simplification methods "Symplify terms" /"Symplify all" can take a long time for large results, so the default is "None". 