1. The problem statement, all variables and given/known data Derive [itex]L_v(u_a)=v^b \partial_b u_a + u_b \partial_a v^b[/itex] 2. Relevant equations [itex]L_v(w^a)=v^b \partial_b w^a - w^b \partial_b v^a[/itex] [itex]L_v(f)=v^a \partial_a f[/itex] where f is a scalar. 3. The attempt at a solution In the end I get stuck with something like this, [itex]L_v(u_a)w^a=v^b u_a \partial_b w^a -u_a v^b \partial_b w^a +v^b w ^a \partial_b u_a +u_a w^b \partial_b v^a [/itex] Which makes me think I am on the right way, but I end up with [itex]L_v(u_a)w^a=v^b w ^a \partial_b u_a +u_a w^b \partial_b v^a [/itex] Which is what I want if I can change place of a and b in the last term only. But I am not allowed to do that just like that right?