f(x) = LN((x + 2)/√(x2 - 4))
= LN(x + 2) - LN(√(x2 - 4))
= LN(x + 2) - LN((x2 - 4)1/2)
= LN(x + 2) - 1/2·LN(x2 - 4)
f'(x) = 1/(x + 2) - 1/2·1/(x2 - 4)·(2·x)
f'(x) = 1/(x + 2) - x/(x2 - 4)
f'(x) = (x - 2)/((x + 2)·(x - 2)) - x/(x2 - 4)
f'(x) = (x - 2)/(x2 - 4) - x/(x2 - 4)
f'(x) = -2 / (x2 - 4)