"Pulling back a function from a neighborhood of 0 in $\mathbb{C}^2$ to $\mathbb{U}$ is analogous to computing the derivative of that function."

Question

I'm reading on Riemann Surfaces and after defining $$\mathbb{U} \equiv \{(z,\ell)\in\mathbb{C}^2\times\mathbb{P}_1;z\in\ell\},$$ and $B\ell_0:\mathbb{U}\to\mathbb{C}^2$, the author mentions that, "Pulling back a function from a neighborhood of 0 in $\mathbb{C}^2$ to $\mathbb{U}$ is analogous to computing the derivative of that function."

I understand what $\mathbb{P}_1$ is but I'm not 100% on the analogy. Is there an intuitive way to understand this?