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

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

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

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

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