Найдите производную функции f (x) = (16-х4) / (х2-4) f (x) = х2/х4+1

Вычислим производную функции:

1) f (x) = (16 - х^4) / (х^2 - 4);

Производная функции равна:

f ' (x) = ((16 - x^4) / (x^2 - 4)) ' = ((16 - x^4) ' * (x^2 - 4) - (x^2 - 4) ' * (16 - x^4)) / (x^2 - 4) ^2 = (-4 * x^3 * (x^2 - 4) - 2 * x * (16 - x^4)) / (x^2 - 4) ^2 = (-4 * x^5 + 16 * x^3 - 32 * x + 2 * x^5) / (x^2 - 4) ^2 = (-2 * x^5 + 16 * x^3 - 32 * x) / (x^2 - 4) ^2;

2) f (x) = х^2 / (х^4 + 1);

f ' (x) = (x^2 / (x^4 + 1)) ' = ((x^2) ' * (x^4 + 1) - (x^4 + 1) ' * x^2) / (x^4 + 1) ^2 = (2 * x * (x^4 + 1) - 4 * x^3 * x^2) / (x^4 + 1) ^2 = (2 * x^5 + 2 * x - 4 * x^5) / (x^4 + 1) ^2 = (2 * x - 2 * x^5) / (x^4 + 1) ^2.