In coordinates, ( σ σ − − 1 ) ∗ ∗ V = ( σ σ − − 1 ) ∗ ∗ V i ∂ ∂ ∂ ∂ u i = V i ∂ ∂ x j ∂ ∂ u i ∂ ∂ ∂ ∂ x j + V i ∂ ∂ τ τ ∂ ∂ u i ∂ ∂ ∂ ∂ τ τ = V i ∂ ∂ x j ∂ ∂ u i ∂ ∂ ∂ ∂ x j + V i ∂ ∂ τ τ ∂ ∂ u i ∂ ∂ ∂ ∂ τ τ = V x j ∂ ∂ ∂ ∂ x j + V τ τ ∂ ∂ ∂ ∂ τ τ .