Отыскать производную: 1)y=arcctg 1/x 2)y=(arcsin x) 3)y=1+sinx 4)y=arctg x/1+x 5)y=(2+cosx) 6)y=arccos(2^x)

1) y = (cos (arctg x)) = (arctg x) * (cos (arctg x)) = (1 / (1 + х^2)) * (-sin (arctg x)) = (-sin (arctg x)) / (1 + х^2);

2) y = (sin (arcctg x)) = (arcctg x) * (sin (arcctg x)) = (1 / (1 + х^2)) * (cos (arcctg x)) = (cos (arcctg x)) / (1 + х^2);

3) y = (sin (arccos x)) = (arccos x) * (sin (arccos x)) = (-1 / (1 - х^2)) * (cos (arccos x)) = (-cos (arccos x)) / (1 - х^2);

4) y = (cos (arcsin x)) = (arcsin x) * (cos (arcsin x)) = (1 / (1 - х^2)) * (-sin (arcsin x)) = (-sin (arcsin x)) / (1 - х^2).

y = (3sin (x^9 sin x) + 7) = (3sin (x^9 sin x)) + (7) = (x^9 sin x) * (3sin (x^9 sin x)) + (7) = ((x^9) (sin x)) * (3sin (x^9 sin x)) + (7) = ((9x^8) cos x) * 3cos (x^9 sin x) + 0 = ((9x^8) cos x) * 3cos (x^9 sin x).

f(x) = (sin^2 (2)) = (2) * (sin (2)) * (sin^2 (2)) = 2 * (cos (2) * 2sin (2) = 4(cos 2)(sin 2).