byproduct

The story

1. Englishby-
2. Proto-Indo-European*per-der.?
3. Proto-Indo-European*pér
4. Proto-Indo-European*pró
5. Proto-Indo-European*pro-
6. Proto-Italic*pro-
7. Latinprō-
8. Proto-Indo-European*dewk-
9. Proto-Indo-European*déwkti
10. Proto-Italic*doukō
11. Latindūcō
12. Latinprōdūcō
13. Latinprōductus
14. Middle Englishproduct
15. Englishproduct
16. English todaybyproduct

From by- + product.