- #1
JohanL
- 158
- 0
the derivative of a tensor
[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?
[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?