1) (a-1) / (2*a+2) + (a+1) / (3-3*a) + (5*a-1) / (3*a^2-3) 2) (2*a+b) / (2*a^2-a*b) - (16*а) / (4*а^2-b^2) + (2*a-b) / (2*a^2+a*b) 3) (y^2-9) / (y^2-6y+9) 4) (b^2-4b+3) / (b^2-9) 5) (z^2-4z-21) / (z^2-6x-7)

Будем использовать:

y = f (g (x)), y' = f'u (u) * g'x (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) ' = u'v + 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)).