The most common and most likely answer to this crossword clue is the 7 plus 10 letter word PARTIAL DERIVATIVE
I've seen this crossword clue in The Times
P
A
R
T
I
A
L
D
E
R
I
V
A
T
I
V
E
Buddy explains!
The straight part
We know that "rate of change" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rate of change = partial derivative.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.