I'm working thorough a proof in a stochastics text and I can't understand how to expand inside an expectation. Could someone give me a hint
\begin{array}{c} \underline{\mathbb{E}\left[\phi\left(X^{\varepsilon}(h), Y^{\varepsilon}(h)\right) \mid X^{\varepsilon}(0)=x, Y^{\varepsilon}(0)=y\right]-\phi(x, y)}{h} \\ =\mathbb{E}\left[\frac{\phi\left(X^{\varepsilon}(h), Y^{\varepsilon}(h)\right)-\phi\left(x, Y^{\varepsilon}(h)\right)}{h} \mid X^{\varepsilon}(0)=x, Y^{\varepsilon}(0)=y\right] \\ +\frac{\mathbb{E}\left[\phi\left(x, Y^{\varepsilon}(h)\right) \mid Y^{\varepsilon}(0)=y\right]-\phi(x, y)}{h} \\ =\mathbb{E}\left[\left(\frac{X^{\varepsilon}(h)-x}{h}\right) \nabla_{x} \phi\left(x, Y^{\varepsilon}(h)\right) \mid X^{\varepsilon}(0)=x, Y^{\varepsilon}(0)=y\right] \\ +\frac{\mathbb{E}\left[\phi\left(x, Y^{\varepsilon}(h)\right) \mid Y^{\varepsilon}(0)=y\right]-\phi(x, y)}{h}+\mathcal{O}(h) \end{array}
of how they have expand $\phi$ in $x$?