1. Найти значение производной функции в точке x0: А) F(x) = 4x / x^2+4 , x0=0 Б) f(x) = 3x*sinx, x0=p/3 2. Найти производную

А) (F(x))\'  = (4x / x^2 + 4)\' =(4 * ( x^2 + 4) - 4x * 2x) / (x^2 + 4)^2

(F(0))\' = 16/ 4^2 = 1.

Б) (f(x))\' = (3x * sin(x))\' = 3 * sin(x) + 3x * cos(x).

(f(π/3))\' = 3 * sin(π/3) + 3 * π/3 * cos(π/3) = 3 * √3/2 + π/2.

2. А) (f(x))\' = (2^(5x + 3))\' = 2^(5x + 3) / ln(2) * (5x + 3)\' = 2^(5x + 3) / ln(2) * 5 .

Б) (f(x))\' = (cos(0,5x + 3))\' = (0,5x + 3)\' * (-sin(0,5x + 3)) = -0,5sin(0,5x + 3);

В) (f(x)) = (√(5x - 1))\' = (5x - 1)\' * 1 / (2√(5x - 1) = 5 / (2√(5x - 1).

Г) (f(x))\' = e^x^2 * 2x + 5.