Найдите производные функций:а) f(x)=1/4x⁴+xб) f(x)=-1/3x²+3x-4в) f(x)=2√x - 2г) f(x)=-5x²+x+1

f(x)\' = (x^2 – 3x + 5)’ = (x^2)’ - (3x)’ + (5)’ = 2 * x^(2 – 1) - 3 * x^(1 – 1) + 0 = 2 * x^1 - 3 * x^0 = 2x – 3.

Ответ: f(x)\' = 2x – 3.

f(x)\' = ((2x + 1) / x)’ = ((2x + 1)’ * x – (2x + 1) * (x)’) / x^2 = (2 * x – (2x + 1) * 1) / x^2 = (2x – 2x – 1) / x^2 = (-1) / x^2.

f(x)\' = (5x^3 + x^2 + x)’ = (5x^3)’ + (x^2)’ + (x)’ = 5 * 3 * x^(3 – 1) + 2 * x^(2 – 1) + 1 * x^(1 – 1) = 15x^2 + 2x^2 + x.

f(x)\' = (2x^3)’ = 2 * 3 * x^(3 – 1) = 6x^2.

f(x)\' = (-x^3 + 3x + 2)’ = (-x^3)’ + (3x)’ + (2)’ = -1 * 3 * x^(3 – 1) + 3 * 1 * x^(1 – 1) + 0 = -3x^2 +3.

f(x)\' = (4 – x^4 – (1 / 3) * x^6)’ = (4)’ – (x^4)’ – ((1 / 3) * x^6)’ = 0 – 4 * x^(4 – 1) – (1 /3) * 6 * x^(6 – 1) = -4x^3 – 2x^5.