Найдите производные функций f(x)=x^2+x^3 f(x)=1/x+5x-2 f(x)=x^2+3x-1 f(x)=x^3+кореньx

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

2) f(x)\' = (tg (x) + сtg (x))’ = (tg (x))’ + (сtg (x))’ = (1 / (cos^2 (x))) + (1 / (-sin^2 (x))) = (1 / (cos^2 (x))) - (1 / (sin^2 (x))).

3) f(x)\' = ((3x^2 - 2) / x^3)’ = ((3x^2 - 2)’ * x^3 - (3x^2 - 2) * (x^3)’) / (x^3)^2 = (((3x^2)’ - (2)’) * x^3 - (3x^2 - 2) * (x^3)’) / x^6 = ((3 * 2 * x - 0) * x^3 - (3x^2 - 2) * (3 * x^2)) / x^6 = (6x^3 – 9x^4 -6x^2) / x^6 = ((x^2) * (6x – 9x^2 -6)) / x^6 = (6x – 9x^2 -6)) / x^4.

4) f(x)\' = ((x^2 + 9) / x)’ = ((x^2 + 9)’ * x - (x^2 + 9) * (x)’) / x^2 = (((x^2)’ + (9)’) * x - (x^2 + 9) * (x)’) / x^2 = ((2x + 0) * x - (x^2 + 9) * 1) / x^2 = (2x^2 - x^2 - 9) / x^2 = (x^2 - 9) / x^2.