а) f (x) = 1/4x^4+7x^3-5x^2+2 b) f (x) = (x^2+5) * (x-3) c) f (x) = (-2x+3) ^8

Найдем производные функций:

а) f (x) = 1/4 * x^4 + 7 * x^3 - 5 * x^2 + 2;

f ' (x) = (1/4 * x^4 + 7 * x^3 - 5 * x^2 + 2) ' = 1/4 * 4 * x^3 + 7 * 3 * x^2 - 5 * 2 * x + 0 = x^3 + 21 * x^2 - 10 * x;

b) f (x) = (x^2 + 5) * (x - 3);

f ' (x) = ((x^2 + 5) * (x - 3)) ' = (x^2 + 5) ' * (x - 3) + (x - 3) ' * (x^2 + 5) = 2 * x * (x - 3) + 1 * (x^2 + 5) = 2 * x^2 - 6 * x + x^2 + 5 = 3 * x^2 - 6 * x + 5;

c) f (x) = (-2 * x + 3) ^8;

f ' (x) = ((-2 * x + 3) ^8) ' = 8 * (-2 * x + 3) ^7 * (-2 * x + 3) ' = 8 * (-2 * x + 3) ^7 * (-2 * 1 + 0) = - 2 * 8 * (-2 * x + 3) ^7 = - 16 * (-2 * x + 3) ^7.