Найти производную функции f(x)=(3√x+2x)⁵ f(x)=(8√+4x²)⁸

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

f(x)\' = ((5x + 1)^(-3))’ = (5x + 1)’ * ((5x + 1)^(-3))’ = ((5x)’ + (1)’) * ((5x + 1)^(-3))’ = (5 + 0) * (-3) * (5x + 1)^(-4) = -15 * (5x + 1)^(-4) = -15 / (5x + 1)^4.