The derivatives of these three invariants with respect to A are ∂ ∂ I 1 ∂ ∂ A = 1 ∂ ∂ I 2 ∂ ∂ A = I 1 1 − − A T ∂ ∂ I 3 ∂ ∂ A = det ( A ) [ A − − 1 ] T = I 2 1 − − A T ( I 1 1 − − A T ) = ( A 2 − − I 1 A + I 2 1 ) T