Learn Finnish: Minun täytyy levätä, jotta tervehdyn pian. - I have to rest so that I get well soon.

The infinitive is tervehtyä (to get well), derived from the adjective terve (healthy). While your current lesson focuses on the -ntua / -ntyä suffix, -htua / -htyä is a very common variant that does the exact same thing: it creates an inchoative verb describing a change of state (becoming healthy).

Why does the t from the infinitive change to a d in tervehdyn?

When you add the first-person ending -n to tervehtyä, the final syllable becomes closed. This triggers consonant gradation, weakening the t to a d. You will need to watch out for this same gradation rule with -ntua / -ntyä verbs, where nt often weakens to nn (for example, parantua becomes parannun).

Why is the subject written as minun instead of minä?

This is a necessive structure. When using the verb täytyy (to have to / must), the subject must be in the genitive case. The verb täytyy never conjugates for the person; it stays frozen in the third-person singular, and the action being done (levätä) stays in the infinitive.

What is the difference between jotta and että in sentences like this?