Autobiography adds auto- to biography. Looking deeper gives three Greek-derived pieces: self, life and writing.
The dictionary suggests a possible German model for this later formation from Greek-derived pieces.
Sources
- Merriam-Webster: autobiography
Word History identifies auto- plus biography and qualifies a possible German model.
- Merriam-Webster: auto-
Combining-form Word History gives the self sense.
- Merriam-Webster: biography
Word History identifies the life and writing formation.
- Merriam-Webster: bio-
Kids combining-form Etymology and definition give life.
- Merriam-Webster: -graphy
Word History and Kids Etymology give writing through Greek and Latin material.
- Online Etymology Dictionary: auto-
Also built on *auto-* "self": autograph