найдите производную функции h (x) = 3/x v (h) = -1/h+3h f (x) = 2/3x+3x^2 f (x) = x^3 (5x-1) (1-2x)

Вычислим производные функций:

1) h (x) = 3/x;

h ' (x) = (3/x) ' = 3 * (1/x) ' = 3 * (1 ' * x - x ' * 1) / x² = 3 * (0 * x - 1 * 1) / x² = 3 * (-1) / x² = - 3/x²;

2) v (h) = - 1/h + 3 * h;

v ' (h) = (-1/n + 3 * n) ' = (-1/n) ' + (3 * n) ' = - * (-1/n²) + 3 * 1 = 1/n² + 3;

3) f (x) = 2/3 * x + 3 * x²;

f ' (x) = (2/3 * x + 3 * x²) ' = (2/3 * x) ' + (3 * x²) ' = 2/3 * 1 + 3 * 2 * x = 2/3 + 6 * x;

4) f (x) = (x^3 * (5 * x - 1) * (1 - 2 * x)) ' = (x^3) ' * (5 * x - 1) * (1 - 2 * x) + x^3 * ((5 * x - 1) * (1 - 2 * x)) ' = 3 * x² * (5 * x - 1) * (1 - 2 * x) + x^3 * (5 * (1 - 2 * x) - 2 * (5 * x - 1)) = 3 * x² * (5 * x - 1) * (1 - 2 * x) + x^3 * (5 + 2) = 3 * x² * (5 * x - 1) * (1 - 2 * x) + 7 * x^3.