Для функции f(x) = cos(6x) - sin(6x) производная f'(x) равна:

• f'(x) = -6sin(6x) - 6cos(6x)

Теперь подставим x = π/8:

• f'(π/8) = -6sin(6 * π/8) - 6cos(6 * π/8)
• f'(π/8) = -6sin(3π/4) - 6cos(3π/4)
• f'(π/8) = -6*(√2/2) - 6*(-√2/2)
• f'(π/8) = -3√2 + 3√2 = 0

Ответ: f'(π/8) = 0