Let $a,b \in \mathbb{C}$. Let $V \subset \mathbb{C}$ be an open neighbourhood of $b$, and let $\varphi: V \to \mathbb{C}$ be holomorphic with $\varphi(b)=a$ and $\varphi'(b)\neq 0$. Let $U \subset \mathbb{C}$ be an open neighbourhood of $a$, and let $f: U \to \mathbb{C}$ be meromorphic. After shrinking $V$ if necessary so that $\varphi(V) \subset U$, the meromorphic differential $f(\varphi(w))\varphi'(w)\,dw$ is defined near $b$, and

\begin{align*} \operatorname{Res}_{w=b}\left(f(\varphi(w))\varphi'(w)\,dw\right)=\operatorname{Res}_{z=a}\left(f(z)\,dz\right). \end{align*}