Вычислите производные 1. f (x) = 2ln*корень sin2x; f=П/8 2. f (x) = arctg*e^-x; f=o 3. f (x) = sin2x (1+cos2x); f=П/44. F (x) = ln*tg^2*2x, f=П/8

1) (f (x)) ' = (2 * ln (√sin (2x)) ' = 2 * (1 / √sin (2x)) * 1/2 * sin^ (-1/2) (2x) * 2 * ( - cos (2x)).

(f (π/8) = 1 / √sin (π/4) * 1 / √sin (π/4) * ( - cos (π/4) = 2/√2 * ( - √2/2) = - 1.

2) (f (x)) ' = (arctg (e^ (-x))) ' = 1 / (1 + e^ (-2x)) * ( - e^ (-x).

(f (0)) ' = - e^0 / (1 + e^0) = - 1/2.

3) (f (x)) ' = (sin2x * (1+cos2x)) ' = 2 * cos (2x) * (1+cos2x) + sin2x * 2 * ( - sin2x) = 2cos (2x) + 2sin (4x).

(f (π/44)) ' = 2cos (π/22) + 2sin (π/11).

4) (f (x)) ' = (ln (tg^2 (2x)) ' = 1 / (tg^2 (2x) * 2tg (2x) * 1/cos^2 (2x) * 2

(f (π/8)) ' = 8