The divergence of a function of three variables is a scalar at each point in space. You can compute the divergence using a formula, but you should also be able to predict the results of such computations directly from the geometric definition of divergence.

You can use the Maple worksheet Visualizing the Divergence or the Mathematica notebook Visualizing the Divergence to compute the divergence of various vector fields, but in each case you should first attempt to predict the answer, then compare your prediction with the computed result.