Найти производную: y=x^3 y=x^2-2 y=-3 y=cosx y=-x^2 y=-2x+5 y=-1/x

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

f(x)\' = ((2x - x^5) / (x – 2))’ = ((2x - x^5)’ * (x – 2) - (2x - x^5) * (x – 2)’) / (x – 2)^2 = (((2x)’ – (x^5)’) * (x – 2) - (2x - x^5) * ((x)’ – (2)’)) / (x – 2)^2 = ((2 - 5x^4) * (x – 2) - (2x - x^5) * (1 – 0)’) / (x – 2)^2 = (2x – 5x^4 + 10x^4 – 2x + x^5) / (x – 2)^2 = (5x^4 + x^5) / (x – 2)^2.

f(x)\' = ((x^2 – 7x + 8)^(-2))’ = (x^2 – 7x + 8)’ * (x^2 – 7x + 8)^(-2)’ = ((x^2)’ – (7x)’ + (8)’) * (x^2 – 7x + 8)^(-2)’ = (2x - 7 + 0) * (-2) * (x^2 – 7x + 8)^(-3) = (14 – 4x) / (x^2 – 7x + 8)^(-3).

f(x)\' = (-√x)’ = (-1 * √x)’ = (-1) * (√x)’ = (-1) * (1 / 2√x) = -1 / 2√x.

f(x)\' = ((x^3 + 1)^4)’ = (x^3 + 1)’ * ((x^3 + 1)^4)’ = ((x^3)’ + (1)’) * ((x^3 + 1)^4)’ = (3x^2 + 0) * 4 * (x^3 + 1)^3 = 12x^2 * (x^3 + 1)^3.