Найти производную функции1. y=( (1+x^2) ) ^ arccos x ; 2.

Будем использовать:

y = f(g(x)), y = fu(u) * gx(x), где u = g(x).

(x^n) = n * x^(n-1).

(c) = 0, где c const.

(c * u) = с * u, где с const.

(sin (x)) = соs (x).

(соs (x)) = -sin (x).

(u v) = u v.

(uv) = uv + uv.

1) f(x) = (sin (x + sin (x)) = (x + sin (x)) * (sin (x + sin (x))) = ((x) + (sin (x))) * (sin (x + sin (x))) = (1 + соs (x)) * соs (x + sin (x)).

2) f(x) = (x^20 sin (x)) = (x^20) (sin (x)) = 20 * x^(20 1) соs (x) = 20x^19 соs (x).

3) f(x) = ((соs (6x^2 + 9))^4) = (6x^2 + 9) * ((соs (6x^2 + 9))^4) = ((6x^2) + (9)) * ((соs (6x^2 + 9))^4) = 12x * 4 * (-sin(6x^2 + 9))^3) = -48x * sin(6x^2 + 9))^3.

4) f(x) = ((соs (x))^2) = (соs (x)) * ((соs (x))^2)= (-sin (x)) * 2 * (соs (x)) = -2 * (sin (x)) * (соs (x)).