Apologies if this seems like a very basic question, but i am tripping quite badly (maybe overstudying). This question relates to applying Ito's lemma on the following portfolio of Φ shares and φ cash:

Vt = Φt St + φt Bt

If I take Ito's Lemma, is the following equation correct?

dVt = Φt dSt + St dΦt + φt dBt + Bt dφt

It seems like I need to add dΦt dSt + dφt dBt but I am not sure why since we are taking partial derivatives?

Thanks in advance for anyone helping my really basic question!

Edit: Just also wanted to ask, if say St or Bt has a higher powers i.e. St\^3 or Bt\^3 in a very odd portfolio for example, does it mean that we need to partially differentiate to St\^2 and Bt\^2 as well?