1. Вычислите (36 49 8 15 )(27

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 (2x 1)) = (2x 1) * (sin (2x 1)) = ((2x) (1)) * (sin (2x 1)) = 2соs (2x 1).

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

3) f(x) = ((sin (x))^2 + (соs (x))^2) = ((sin (x))^2) + ((соs (x))^2) = (sin (x)) * ((sin (x))^2) + (соs (x)) * ((соs (x))^2)= 2 * (соs (x)) * (sin (x)) 2 * (sin (x)) * (соs (x)) = 0.

4) 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.

5) f(x) = ((соs (x))^4) = (соs (x)) * ((соs (x))^4)= (-sin (x)) * 4 * (соs (x))^3 = -4 * (sin (x)) * (соs (x))^3.

6) f(x) = (8x^3 5x^2 4x + 2) = (8x^3) (5x^2) (4x) + (2) = 8 * 3 * x^2 5 * 2 * x 4 + 0 = 24x^2 10x 4.