$derived from multiple children own $derived

My svelte 5 app has a "tree" like structure, with a global $state rune.The app will load its components according to the current state.

If a user input a value in a "leaf" component, a $derived rune will compute that input.

But then in the parent branch we'd like to have a $derived from all the branch's leafs own $derived computation.

Hopefully, achieving granular recomputation only when the right state value is changed.

Can I even do that with runes ?

Here is a REPL of the idea:https://svelte.dev/playground/de29facccf8646718fa0074d906df67b?version=5.19.9