Найти производные 1. Y=sinx/e^x 2.y=cos^4*2x 3.y=tg(4x-5)

1) f(х)\' = (sin^3 (2 - 3х))’ = (2 - 3х)’ * (sin (2 - 3х))’ * (sin^3 (2 - 3х))’ = ((2)’ – (3х)’) * (sin (2 - 3х))’ * (sin^3 (2 - 3х))’ = (0 – 3) * (соs (2 - 3х)) * 3 * (sin^2 (2 - 3х)) = (-3) * (соs (2 - 3х)) * 3 * (sin^2 (2 - 3х)) = (-9) * (соs (2 - 3х)) * (sin^2 (2 - 3х).

2) f(х)\' = (соs^2 (х / 3))’ = (х / 3)’ * (соs (х / 3))’ * (соs^2 (х / 3))’ = (1 / 3) * (-sin (х / 3)) * 2 * (соs (х / 3)) = (2 / 3) * (-sin (х / 3)) * (соs (х / 3)).

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