Let (mathbf{F}) and (mathbf{G}) be vector fields. Prove the the following Product Rule for Divergence: [ operatorname{div}(mathbf{F}
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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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This identity often referred to as the divergence theorem is one of the fundamental identities in ve...View the full answer
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