# Explanation of delta method?

Definition: For $A\subset\mathbb{R}, X_n$ are A-valued random variables and $a_n (X_n - \theta) \stackrel{D}{\rightarrow} X$ for some sequence $\{a_n\}_{n\in\mathbb{N}}$ satisfying $a_n \rightarrow \infty$ as $n \rightarrow \infty$. Then for any function $h: A \rightarrow\mathbb{R}$ that is differentiable at $\theta , a_n (h(X_n ) - h(\theta)) \stackrel{D}{\rightarrow} h'(\theta)X$