Question

Найти значение f ' (π/12), если f(x)=sin^4x - cos^4x

Answer 1

f'(x) = 4sin^3xcosx + 4cos^3xsinx = 4 sinx cosx(sin^2x + cos^2x) = 2sin2x. f'(pi/12) = 2sin(pi/6) = 2*1/2 = 1. Ответ: 1.