Generator of function of Markov process

Question

Let $X_t$ be a Markov process with generator $\mathcal{A}f(x) = a f''(x) + bf'(x)$.

For $\phi(x)\in C^2(\mathbb{R})$, we define $Y_t = \phi(X_t)$.

Definition of generator is as follows

$ \mathcal{A}f(x) := \lim_{t\downarrow0}\frac{\mathbb{E}[f(X_t)|X_0 = x] − f(x)}{t}$.

Using definition of generator find generator of $Y_t$?

Any ideas?