1. Отыскать значение производной функции в точке x0: А) F(x) =

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(/3)) = 3 * sin(/3) + 3 * /3 * cos(/3) = 3 * 3/2 + /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.