F(x)=3x^4-12x-2 f(x)=2/х^10-x^2/8+8√x f(x)=(x+2)/sinx f(x)=(5-x)/cosx f(x)=(6x^2-3)*(x+2)

1) (F(x))\' = (3x^4)\' - (12x)\' - (2)\' = 3 * 4 * x^3 - 12 = 12(x^3 - 1).

2) (f(x))\' = (2 / x^10)\' - (x^2 / 8)\' + (8√x)\' = 2 * (-10) * x^(-11) - 2x / 8 + 8 *1/2 * x^(-1/2). 

3) (f(x))\' = ((x + 2)\' * sin(x) - (x + 2) * (sin(x))\') / sin^2(x) = 1 / sin(x) + (x + 2) * cos(x) / sin^2(x).

4)  (f(x))\' = ((5 - x)\' * cos(x) - (5 - x) * (cos(x))\') / cos^2(x) = -1 / cos(x) - (5 - x) * sin(x) / cos^2(x).

5) (f(x))\' = (6x^2 - 3)\' * (x + 2) + (x + 2)\' * (6x^2 - 3) = 12x * (x + 2) + 6x^2 - 3) = 16x^2 + 24x - 3.