- #1

member 428835

## Homework Statement

Show $$\frac{\partial \det(A)}{\partial A_{pq}} = \frac{1}{2}\epsilon_{pjk}\epsilon_{qmn}A_{jm}A_{kn}$$

## Homework Equations

##\det(A)=\epsilon_{ijk}A_{1i}A_{2j}A_{3k}##

## The Attempt at a Solution

$$\frac{\partial \det(A)}{\partial A_{pq}}=\frac{\partial}{\partial A_{pq}}\epsilon_{ijk}A_{1i}A_{2j}A_{3k}\\

=\epsilon_{ijk}\frac{\partial}{\partial A_{pq}}A_{1i}A_{2j}A_{3k}$$

but I'm now stuck. I feel like one of the ##A## components on the RHS must go to 1 and the rest would be constant, leaving some sort of ##\epsilon A_{yy} A_{xx}## behind. I'm thinking along the lines of ##\partial A_{ij}/\partial A_{ik} = \delta_{jk}##. Any ideas?