Y=(3+х)/2 * (х(2-ч))^1/2 + 3 arccos(х/2)^1/2 производная

y\' = ((cos^2 х) * (1 / х))’ = (cos^2 х)’ * (1 / х) + (cos^2 х) * (1 / х)’ = (cos х)’ * (cos^2 х)’ * (1 / х) + (cos^2 х) * (1 / х)’ = (-2 * (sin х) * (cos х) * (1 / х)) + (cos^2 х) * (-1 / х^2) = (-2(sin х)(cos х) / х) + (cos^2 х / х^2).

f(х)\' = (х * (х – 4))’ = (х)’ * (х – 4) + х * (х – 4)’ = (х)’ * (х – 4) + х * ((х)’ – (4)’) = 1 * (х – 4) + х * (1 – 0) = х – 4 + х = 2х – 4.

f(х)\' = (3 * (2 – х)^6)’ = 3 * (2 – х)’ * ((2 – х)^6)’ = 3 * ((2)’ – (х)’) * ((2 – х)^6)’ = 3 * (0 – 1 * х^(1 – 1)) * 6 * (2 – х)^(6 - 1) = 3 * (0 – 1) * 6 * (2 – х)^5 = 3 * 6 * (2 – х)^5 = 18(2 – х)^5.

f(х)\' = ((х^2) / (х + 3))’ = ((х^2)’ * (х + 3) – (х^2) * (х + 3)’) / (х + 3)^2 = ((х^2)’ * (х + 3) – (х^2) * ((х)’ + (3)’)) / (х + 3)^2 = (2х * (х + 3) – (х^2) * (1 + 0)) / (х + 3)^2 = (2х^2 + 6х – х^2) / (х + 3)^2 = (х^2 + 6х) / (х + 3)^2.

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