I am following a physics paper that uses linear perturbation theory. They take steps that imply things such as
$$\delta\left( \frac{1}{y} \right) = -\frac{\delta y}{y^2}$$
where $\delta$ is a small linear perturbation and $y$ is some function. It looks to me a bit like the second term in a Taylor series expansion, but I'm struggling to connect the dots.
What are the "rules" of the $\delta$ operator? Is there a text that gives its properties?