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Collecting coefficients of derivatives

I have a complicated expression involving derivatives of a function, and I'd like to collect all of the first, second, third, etc. derivatives. For example, my expression starts:

a1*a2*a3*x*f(x) + a1*a2*x^2*diff(f(x), x) + a1*a3*x^2*diff(f(x), x) + a2*a3*x^2*diff(f(x), x)

and I would like to rewrite that part as

    a1*a2*a3*x*f(x) + (a1*a2*x^2*+ a1*a3*x^2+ a2*a3*x^2)*diff(f(x), x)

How do I tell Sage to do this?