There is a comment to this effect in Revuz and Yor's *Continuous Martingales and Brownian Motion* after the proof for continuous semimartingale vector $X=(X^1,\dots,X^d)$ and $F\in C^2$ (pg 147):

> **Remark 1°)** The differentiability properties of $F$ may be somewhat relaxed. For instance, if some of the $X^{i}$'s are of finite variation, $F$ needs only be of class $C^1$ in the corresponding coordinates; the proof goes through just the same.