The vectors x and c can be written as x = x i e i and c = c i e i . Let y := x + α c. In that case the gradient is given by ∇ ∇ T ⋅ ⋅ c = d d α α T ( x 1 + α α c 1 , x 2 + α α c 2 , x 3 + α α c 3 ) | α α = 0 ≡ ≡ d d α α T ( y 1 , y 2 , y 3 ) | α α = 0 = [ ∂ ∂ T ∂ ∂ y 1 ∂ ∂ y 1 ∂ ∂ α α + ∂ ∂ T ∂ ∂ y 2 ∂ ∂ y 2 ∂ ∂ α α + ∂ ∂ T ∂ ∂ y 3 ∂ ∂ y 3 ∂ ∂ α α ] α α = 0 = [ ∂ ∂ T ∂ ∂ y 1 c 1 + ∂ ∂ T ∂ ∂ y 2 c 2 + ∂ ∂ T ∂ ∂ y 3 c 3 ] α α = 0 = ∂ ∂ T ∂ ∂ x 1 c 1 + ∂ ∂ T ∂ ∂ x 2 c 2 + ∂ ∂ T ∂ ∂ x 3 c 3 ≡ ≡ ∂ ∂ T ∂ ∂ x i c i = ∂ ∂ T ∂ ∂ x i ( e i ⋅ ⋅ c ) = [ ∂ ∂ T ∂ ∂ x i ⊗ ⊗ e i ] ⋅ ⋅ c ◻ ◻