Question: Let (f) be a scalar function and (mathbf{F}) be a vector field. Prove the following Product Rule for Divergence: [ operatorname{div}(f mathbf{F})=f operatorname{div}(mathbf{F})+abla f cdot

Let $f$ be a scalar function and $\mathbf{F}$ be a vector field. Prove the following Product Rule for Divergence:
\[
\operatorname{div}(f \mathbf{F})=f \operatorname{div}(\mathbf{F})+abla f \cdot \mathbf{F}
\]

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