Differentiating this with respect to q ˙ ˙ l , l ∈ ∈ [ 1 , n ] , gives ∂ ∂ T ( q , q ˙ ˙ ) ∂ ∂ q ˙ ˙ l = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( ∂ ∂ [ c i j ( q ) q ˙ ˙ i q ˙ ˙ j ] ∂ ∂ q ˙ ˙ l ) = ∑ ∑ i = 1 n ∑ ∑ j = 1 n ( c i j ( q ) ∂ ∂ [ q ˙ ˙ i q ˙ ˙ j ] ∂ ∂ q ˙ ˙ l )