The most common and most likely answer to this crossword clue is the 9 letter word OFFSHOOTS
I've seen this crossword clue in The Daily Telegraph
O
F
F
S
H
O
O
T
S
More clues leading to the result OFFSHOOTS
Buddy explains!

The straight part
We know that "derivatives" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case derivatives = offshoots.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OFFSHOOTS mean?
OFFSHOOTS noun- That which shoots off or separates from a main stem or branch of a plant.
- That which develops from something else.