Найдите производную функции: А) y=ctg2x B) y=√x*sinx C) y=cos^2x

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

f(х)\' = (cos (2х) – sin (3х))’ = (cos (2х))’ – (sin (3х))’ = (2х)’ * (cos (2х))’ – (3х)’ * (sin (3х))’ = = -2sin (2х) - 3cos (3х).

f(х)\' = (х^3 * sin (2х))’ = (х^3)’ * sin (2х) + х^3 * (sin (2х))’ = (х^3)’ * sin (2х) + х^3 * (2х)’ * (sin (2х))’ = 3х^2 * sin (2х) + х^3 * 2 * cos (2х) = 3х^2sin (2х) + 2х^3cos (2х).

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