- #1

- 302

- 0

## Main Question or Discussion Point

Hello.

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.

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.