First of all I have to apologize for a probably not conforming style, this is my first own-written discussion so please be patient.
Problem:
The argumentation for
because of
doesn't sound reasonable to me.
I think this argument only leads to
![{\displaystyle \left({\frac {\partial e}{\partial {\boldsymbol {E}}}}\right)^{T}+{\frac {\partial e}{\partial {\boldsymbol {E}}}}={\frac {\partial e}{\partial {\boldsymbol {E}}}}+\left({\frac {\partial e}{\partial {\boldsymbol {E}}}}\right)^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/004cf3d3e3cae0201fa1d76e30e2e120bb53e0db)
what is obviously not helpful.
Proposal for Solution:
In my opinion one should argue that
is symmetric and therefore
what gives the demanded symmetry.