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

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