[tongkub]

f'(x) = (x-1)'(x-2(...) + ... + (x - 10)(x-11)'

f'(7) = (....)(7 - 7)(7-8) + 0 + 0 +0 +... + (7-1)(7-2)(7-3)(7-4)(7-5)(7-6)(7-8)(7-9)(7-10)(7-11) + 0 + 0 + 0 +... + 0

f'(7) = (6)(5)(4)(3)(2)(1)(-1)(-2)(-3)(-4) = (6!)(4!) = (720)(24) = 17280