Diff does not work in fraction field

Given a polynomial ring like
P=QQ[t1,t2,t3]

and its field of fractions

F=QQ(t1,t2,t3)

if we have a function f in F, we ought to be able to take the derivative with diff by the quotient rule.

Something like

diffq:= (var,f)-> (
num:=numerator(f);
den:=denominator(f);
varn:=sub(var,ring num);
newf=(den_diff(varn,num)-num_diff(varn,den))/(den^2)
)

worked for me.

Start by locating the diff entry point for elements of a fraction field, then compare its handling with the numerator, denominator, and quotient-rule example in the issue. Done means diff accepts a function in QQ(t1,t2,t3) and returns the expected derivative without requiring the workaround; add or run a regression case for that example.

Written by the indexing model from the issue text.