How Does Symmetry Impact the Derivative in Tensor Calculations?

[adriang]

Homework Statement

If $$\phi=a_{rs}x^{r}x^{s}$$
Then show that $$\frac{\partial\phi}{\partial x^{r}}=(a_{rs}+a_{sr})x^{s}$$

Homework Equations

The Attempt at a Solution

Help please I can't seem to get the correct answer. Thanks

 

[tiny-tim]

hi adriang!

you have to remember that once you've summed over an index, you can't use it again!

in this case, you can't write ∂/∂x^r (a_rsx^rx^s) …

instead try writing ∂/∂x^r (a_qsx^qx^s) ​

 

[adriang]

ah thanks tim lol silly me..