The most common and most likely answer to this crossword clue is the 4 plus 1 plus 5 plus 5 letter word HAVE A SLATE LOOSE
I've seen this crossword clue in The Daily Telegraph
H
A
V
E
A
S
L
A
T
E
L
O
O
S
E
Buddy explains!
The straight part
We know that "Be slightly deranged" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case be slightly deranged = have a slate loose.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.