How to mark non-pre-defined functions as functions of a certain variable during calculation of derivative?

If I have some calculation $$X=v\cdot\delta$$ and I want to calculate $$\frac{\partial}{\partial v}X$$, the result according to Mathematica is $$\delta$$. Now, I want to define $$\delta$$ as a function of $$v$$ but without defining the exact formula because I do not have that as a whole but numerically. Thus, I want the result to be $$\frac{\partial}{\partial v}X=\delta+v\frac{\partial \delta}{\partial v}$$ which is just the application of the product formula for derivatives. How to set some kind of a "flag" or "marker" to prevent Mathematica from deriving $$\delta$$ after $$v$$ and saying that the result is always $$0$$ because the variables are named differently?

You can use Dt:

Dt[v δ, v]


δ + v Dt[δ, v]

Or D with the option NonConstants:

D[v δ, v, NonConstants -> {δ}]


δ + v D[δ, v, NonConstants -> {δ}]