Найдите производную функцию a) f (x) = (x^2+1/x^2) ^9 б) f (x) = 2/x^2-√x B) f (x) = (x^5-4/x) ^11 г) fx) = 1/2x+√ x

Question

Матвей Белов

Математика

12 марта, 04:25

Найдите производную функцию a) f (x) = (x^2+1/x^2) ^9 б) f (x) = 2/x^2-√x B) f (x) = (x^5-4/x) ^11 г) fx) = 1/2x+√ x

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София Сорокина · Answer 1

(x) ' = (x^2 * ctg (x)) ' = (x^2) ' * ctg (x) + x^2 * (ctg (x)) ' = 2x * ctg (x) + x^2 * (1 / (-sin^2 (x))) = 2xctg (x) - x^2 / (sin^2 (x)).

f (x) ' = (x^2 * tg (x)) ' = (x^2) ' * tg (x) + x^2 * (tg (x)) ' = 2x * tg (x) + x^2 * (1 / (cos^2 (x))) = 2xtg (x) + x^2 / (cos^2 (x)).

f (x) ' = (sin^2 (x)) ' = (sin (x)) ' * (sin^2 (x)) ' = cos (x) * 2 * sin^ (2 - 1) (x) = cos (x) * 2 * sin^ (1) (x) = cos (x) * 2 * sin (x) = 2cos (x) sin (x).

f (x) ' = (tg (x) - сtg (x)) ' = (tg (x)) ' - (сtg (x)) ' = (1 / (cos^2 (x))) - (1 / (-sin^2 (x))) = (1 / (cos^2 (x))) + (1 / (sin^2 (x))).