Material derivatives are differentiated before commuting the drift.

theorem AVenhance.Infra.Section4.iterate_classical_word_material_gradient_equation {b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2} {κ : ℝ} {F u : ℝ → Homogenization.Vec 2 → ℝ} {u₀ : Homogenization.Vec 2 → ℝ} (hsol : IsClassicalSol b κ F u₀ u) {t : ℝ} (ht : 0 < t) (hF : ContDiff ℝ (↑⊤) (F t)) (w : List (Fin 2)) (x : Homogenization.Vec 2) (j : Fin 2) : spaceGrad (iterateSpatialWord w (amnrMaterial b u t)) x j = κ * spaceLap (fun (y : Homogenization.Vec 2) => spaceGrad (iterateSpatialWord w (u t)) y j) x + spaceGrad (iterateSpatialWord w (F t)) x j

The differentiated current material field has only the differentiated original forcing on its right side. Drift commutators are kept separately.