Identity 5:
The left side is the divergence of the product , where is a scalar and F is a vector, both in spherical coordinates. From Table 9.3.2, the resulting scalar is
The first term on the right is the product of the scalar and the divergence of F. From Table 9.3.2, the resulting scalar is
The second term on the right is the dot product of F with the gradient of . From Table 9.3.2, the resulting scalar is
The sum of the terms on the right is then