Splitting the summation, evaluating the partial derivative, and rejoining the summation gives ∂ ∂ T ( q , q ˙ ˙ ) ∂ ∂ q ˙ ˙ l = ∑ ∑ i ≠ ≠ l n ∑ ∑ j ≠ ≠ l n ( c i j ( q ) ∂ ∂ [ q ˙ ˙ i q ˙ ˙ j ] ∂ ∂ q ˙ ˙ l ) + ∑ ∑ i ≠ ≠ l n ( c i l ( q ) ∂ ∂ [ q ˙ ˙ i q ˙ ˙ l ] ∂ ∂ q ˙ ˙ l ) + ∑ ∑ j ≠ ≠ l n ( c l j ( q ) ∂ ∂ [ q ˙ ˙ l q ˙ ˙ j ] ∂ ∂ q ˙ ˙ l ) + c l l ( q ) ∂ ∂ [ q ˙ ˙ l 2 ] ∂ ∂ q ˙ ˙ l = ∑ ∑ i ≠ ≠ l n ∑ ∑ j ≠ ≠ l n ( 0 ) + ∑ ∑ i ≠ ≠ l n ( c i l ( q ) q ˙ ˙ i ) + ∑ ∑ j ≠ ≠ l n ( c l j ( q ) q ˙ ˙ j ) + 2 c l l ( q ) q ˙ ˙ l = ∑ ∑ i = 1 n ( c i l ( q ) q ˙ ˙ i ) + ∑ ∑ j = 1 n ( c l j ( q ) q ˙ ˙ j )