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5. Use Levi-Cività symbol to prove that \text { (a) } \nabla \cdot(f \mathrm{~g})=f \nabla \cdot \mathrm{g}+\mathrm{g} \cdot \nabla f \text { (b) } \nabla \times(f g)=f \nabla \times g-g \times \nabla f \text { (c) }(\mathbf{A} \times \mathbf{B}) \cdot(\mathbf{C} \times \mathbf{D})=(\mathbf{A} \cdot \mathbf{C})(\mathbf{B} \cdot \mathbf{D})-(\mathbf{A} \cdot \mathbf{D})(\mathbf{B} \cdot \mathbf{C}) \text { (d) } \nabla \cdot(f \times g)=g \cdot(\nabla \times f)-f \cdot(\nabla \times g)

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