In simpler form, using Feynman subscript notation:

where the notation ∇ means the subscripted gradient operates on only the factor A.

A less general but similar idea is used in "geometric algebra" where the so-called Hestenes "overdot notation" is employed. The above identity is then expressed as:

where overdots define the scope of the vector derivative. In the first term it is only the first (dotted) factor that is differentiated, while the second is held constant. Likewise, in the second term it is the second (dotted) factor that is differentiated, and the first is held constant.

As a special case, when A = B:

Divergence of the curl
Vector dot product
किसी अदिश क्षेत्र का ग्रेडिएंट (Gradient of a scalar field)
Product rule for the gradient