Therefore, if the tensor A is symmetric, then the derivative is also symmetric and we get ∂ ∂ A ∂ ∂ A = I ( s ) = 1 2 ( I + I T ) where the symmetric fourth order identity tensor is I ( s ) = 1 2 ( δ δ i k δ δ j l + δ δ i l δ δ j k ) e i ⊗ ⊗ e j ⊗ ⊗ e k ⊗ ⊗ e l