# Is an exponential function of a stochastic process a smooth function?

Let's say I have an Ito process $$X_t$$, and another process $$Y_t=e^{\int_t^{t+\delta} X_s ds}$$. I want to know that quadratic variation of $$Y_t$$ and another process.

I know that the quadratic variation of a smooth function, with any other function is $$0$$, but I'm wondering if $$Y_t$$ counts as a smooth function in this case, since it is a function of a stochastic process $$X_t$$, rather than being a function of $$s$$: $$e^{\int f(s) ds}$$. So, is the quadratic variation of $$Y_t$$ with another process, $$=0$$ even though it is a function of a random varible $$X_t$$? Or not necessarily?