In \mathbb{R}^3 let E_1, \ E_2, \ E_3 be a frame field, with W=\sum f_iE_i, show that \nabla_V W=\sum_j \bigg{(}\nabla_Vf_i+\sum_i f_i\omega_{ij}(V)\bigg{)}E_j

So what I have so far is: \nabla_V W=\nabla_V \sum f_iE_i = E_i\nabla_V\sum f_i+\sum f_i\nabla_V E_i

now I have that \omega_{ij} is the connection forms of the frame field E_1, \ E_2, \ E_3 then \nabla_V E_i = \sum_j \omega_{ij}(V)E_j so I have:

\nabla_V W=\nabla_V \sum f_iE_i = E_i\nabla_V\sum f_i+\sum f_i\nabla_V E_i = {\color{blue}E_i\nabla_V\sum f_i+\sum_i f_i\sum_j \omega_{ij}(V)E_j} \neq \sum_j \bigg{(}\nabla_Vf_i+\sum_i f_i\omega_{ij}(V)\bigg{)}E_j

I can't seem to get to to equal one another.