Найти производную функции: 1. y=x lnx - (x+1)^1/4 2. y=2x^2-x-1/3 корень2+4x ^ - степень / - деление

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).

f(x)\' (1) = -2 – 3 * 1 = -2 – 3 = -5.

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

f(x)\' = (3 * (2 – x)^6)’ = 3 * (2 – x)’ * ((2 – x)^6)’ = 3 * ((2)’ – (x)’) * ((2 – x)^6)’ = 3 * (0 – 1 * x^(1 – 1)) * 6 * (2 – x)^(6 - 1) = 3 * (0 – 1) * 6 * (2 – x)^5 = 3 * 6 * (2 – x)^5 = 18(2 – x)^5.