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I was messing around with subscript summation notation problems, and I ended up trying to determine a vector identity for the following expresion:

[tex]\overline{\nabla}(\overline{A}\cdot\overline{B})[/tex]

Here are my steps for as far as I got:

[tex]\hat{e}_{i}\frac{\partial}{\partial x_{i}}(A_{j}\hat{e}_{j}\cdot B_{k}\hat{e}_{k})[/tex]

[tex]\hat{e}_{i}\frac{\partial}{\partial x_{i}}(A_{j}B_{k}\delta_{jk})[/tex]

[tex]\hat{e}_{i}\frac{\partial}{\partial x_{i}}(A_{j}B_{j})[/tex]

[tex]\hat{e}_{i}(A_{j}\frac{\partial B_{j}}{\partial x_{i}} +B_{j}\frac{\partial A_{j}}{\partial x_{i}} )[/tex]

After these steps, I could not clearly see any ways to continue to manipulate this expression.

Not knowing whether an identity actually existed for this expression, I turned to wikipedia and they suprisingly had the solution (which was more complicated than I thought it would have been.)

Regardless, I wasn't sure what steps could be taken to arrive at the solution.

Thanks,

pcalhoun

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# Gradient of a Vector Dot Product

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