Gradient, Divergence and Curl

Del, or nabla, is an vector differential operator, usually represented by the nabla symbol ∇.  

The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, a dot product, and a cross product, respectively, of the del "operator" with the field. 

These formal products do not necessarily commute with other operators or products. These three uses, detailed below, are summarized as:

• Gradient:  
• Divergence:
• Curl: