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[tex]

a_{ij}x^ix^j

[/tex]

with respect to [tex]x^k[/tex], k=2 and i,j = 1,2,3.

solution:

[tex]

\frac {d} {dx^k}a_{ij}x^ix^j =

a_{ij}\frac {dx^i} {dx^k}x^j + a_{ij}x^i \frac {dx^j} {dx^k} =

a_{2j}x^j + a_{i2}x^i =

a_{21}x^1 + a_{22}x^2 + a_{23}x^3 + a_{12}x^1 + a_{22}x^2 + a_{32}x^3

[/tex]

is that correct?