Найдите производные функций f(x)=x^3(4+2x-x^2) f(x)=x^2(3x+x^3) f(x)=√x(2x^2-x) f(x)=(2x-3)(1-x^3)

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

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

y\' (3π / 4) = 3 * cos (3 * (3π / 4)) + 3 * sin (3 * (3π / 4)) = 3 * cos (9π / 4) + 3 * sin (9π / 4) = 3 * cos (2π + (π / 4)) + 3 * sin (2π + (π / 4)) = 3 * cos (π / 4) + 3 * sin (π / 4) = 3 * (cos (π / 4) + sin (π / 4)) = 3 * ((√2 / 2) + (√2 / 2)) = 3 * √2 = 3√2.

y’ = (cos (arcsin x))’ = (arcsin x)’ * (cos (arcsin x))’ = (1 / √(1 - х^2)) * (-sin (arcsin x)) = (-sin (arcsin x)) / √(1 - х^2).