Производные от обратной функции y=1-arctgx y=arcsinx/a y=arctgx/a y=arccos(1-2x) y=arctg1+x/1-x y=arccos(1-x^2)

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

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

f(х)’ = (sin (х) – cos (х))’ = (sin (х))’ – (cos (х))’ = cos (х) – (-sin (х)) = cos (х) + sin (х).

f(х)\' = (х * sin (2х + 1))’ = (х)’ * sin (2х + 1) + х * (sin (2х + 1))’ = (х)’ * sin (2х + 1) + х * (2х + 1)’ * (sin (2х + 1))’ = (х)’ * sin (2х + 1) + х * ((2х)’ + (1)’) * (sin (2х + 1))’ = 1 * sin (2х + 1) + х * (2 + 0) * cos (2х + 1) = sin (2х + 1) + 2хcos (2х + 1).