If $f\colon M\rightarrow\mathbf{On}$ is a function from any set of ordinals to the class of ordinals then $\operatorname{Fix}(f)=\{x\in M\mid f(x)=x\}$ is the set of fixed points of $f$ $f^\prime$ the derivative of $f$ is the enumerating function of $\operatorname{Fix}(f)$

If $f$ is $\kappa$ normal then $\operatorname{Fix}(f)$ is $\kappa$ closed and $\kappa$ normal, and therefore $f^\prime$ is also $\kappa$ normal.

For example, the function which takes an ordinal $\alpha$ to the ordinal $1+\alpha$ has a fixed point at every ordinal $\geq\omega$ so $f^\prime(\alpha)=\omega+\alpha$