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How can I prove something like

[tex]

\nabla\cdot(\mathbf fv)=(\nabla v)\cdot\mathbf f+v(\nabla\cdot \mathbf f)

[/tex]

using only the definition of divergence

[tex]

\text{div}\mathbf V=\lim_{\Delta v\rightarrow0}\frac{\oint_S\mathbf V\cdot d\mathbf s}{\Delta v},

[/tex]

i.e. without referring to any particular coordinate system? I have yet to see a book that does not assume cartesian coordinates.

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# Vector calculus identities proof

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