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.