Chapter 15 - Topics In Vector Calculus - 15.1 Vector Fields - Exercises Set 15.1 - Page 1093: 39

See explanation

1. \(\nabla \cdot (\mathbf{k} \mathbf{A}) = k \nabla \cdot \mathbf{A}\) 2. \(\nabla \cdot (\mathbf{A} + \mathbf{B}) = \nabla \cdot \mathbf{A} + \nabla \cdot \mathbf{B}\) 3. \(\nabla \cdot (\phi \mathbf{F}) = \phi \nabla \cdot \mathbf{F} + \nabla \phi \cdot \mathbf{F}\) 4. \(\nabla \cdot (\nabla \times \mathbf{F}) = 0\)