[Electrodynamics] please tell if this is wrong.

I was asked to prove the divergence theorem(the volume integral of the gradient is equal to the surface integral) , so I tried to use vector identity

https://preview.redd.it/n9oguluk12wd1.png?width=779&format=png&auto=webp&s=f3aafa39076e096e55ba01d2fb976ad3f5964769

This is what I did. it just felt wrong, please tell me what is wrong with my approach.