найдите производные функций:1) f(x)=cosx² 2) f(x)=sinx² 3) f(x)=tg³(2-3x) 4) f(x)=ctg⁴(2x-1) Вычислите значение производной

f(x)\' = ((sin (x))^(-1))’ = (sin (x))’ * ((sin (x))^(-1))’ =

(cos (x)) * (-1) * ((sin (x))^(-2)) = (-cos (x)) / ((sin (x)^2).

f(x)\' = (tg (3x))’ = (3x)’ * (tg (3x))’ = 3 * (1 / (cos^2 (3x))) = 3 / (cos^2 (3x)).

f(x)\' = (sin (6x^4 - 2x^2 + 3))’ = (6x^4 - 2x^2 + 3)’ * (sin (6x^4 - 2x^2 + 3))’ = ((6x^4)’ – (2x^2)’ + (3)’) * (sin (6x^4 - 2x^2 + 3))’ = (6 * 4 * x^3 – 2 * 2 * x + 0) * cos (6x^4 - 2x^2 + 3).

f(x)\' = (sin^2 (x))’ = (sin (x))’ * (sin^2 (x))’ = cos (x) * 2 * sin^(2 – 1) (x) = cos (x) * 2 * sin^(1) (x) = cos (x) * 2 * sin (x) = 2cos (x) sin (x).

f(x)\' = (tg (x) - сtg (x))’ = (tg (x))’ – (сtg (x))’ = (1 / (cos^2 (x))) – (1 / (-sin^2 (x))) = (1 / (cos^2 (x))) + (1 / (sin^2 (x))).