Question: Let (mathbf{F}) and (mathbf{G}) be vector fields. Prove the the following Product Rule for Divergence: [ operatorname{div}(mathbf{F} times mathbf{G})=operatorname{curl}(mathbf{F}) cdot mathbf{G}-mathbf{F} cdot operatorname{curl}(mathbf{G}) ]

Let $\mathbf{F}$ and $\mathbf{G}$ be vector fields. Prove the the following Product Rule for Divergence:
\[
\operatorname{div}(\mathbf{F} \times \mathbf{G})=\operatorname{curl}(\mathbf{F}) \cdot \mathbf{G}-\mathbf{F} \cdot \operatorname{curl}(\mathbf{G})
\]

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