f(x) = ctg3x/3

f'(x) = -(3x)'/3sin^2 (3x) = -3/3sin^2 (3x) = -1/sin^2 (3x)

f'(x0) = f(-π/6) = -1/sin^2 (3(-π/6)) = -1/sin^2 (-π/2) = -1/1 = -1

Ответ : -1