What is the derivative of $\partial A/\partial ({A^T}A)$ ? Where $A$ is a 3x3 tensor.
(in index notation, I want to find explicit components of ${D_{ijpq}} = \partial {A_{ij}}/\partial ({A_{kp}}{A_{kq}})$ )
Attempt:
I have tried through inverse way using the chain rule as below:
$\frac{{\partial \left( {{A_{kp}}{A_{kq}}} \right)}}{{\partial {A_{ij}}}} = \left( {{A_{iq}}{\delta _{jp}} + {A_{ip}}{\delta _{jq}}} \right)$
but as its inverse is not attainable, I think other manipulation is required.
Any comment would be much appreciated!