F (x) = 3x^4-12x-2 f (x) = 2/х^10-x^2/8+8√x f (x) = (x+2) / sinx f (x) = (5-x) / cosx f (x) = (6x^2-3) * (x+2)

Question

Роберт Рыбаков

Математика

10 июля, 09:26

F (x) = 3x^4-12x-2 f (x) = 2/х^10-x^2/8+8√x f (x) = (x+2) / sinx f (x) = (5-x) / cosx f (x) = (6x^2-3) * (x+2)

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Тимофей Блохин · Answer 1

1) (F (x)) ' = (3x^4) ' - (12x) ' - (2) ' = 3 * 4 * x^3 - 12 = 12 (x^3 - 1).

2) (f (x)) ' = (2 / x^10) ' - (x^2 / 8) ' + (8√x) ' = 2 * (-10) * x^ (-11) - 2x / 8 + 8 * 1/2 * x^ (-1/2).

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

4) (f (x)) ' = ((5 - x) ' * cos (x) - (5 - x) * (cos (x)) ') / cos^2 (x) = - 1 / cos (x) - (5 - x) * sin (x) / cos^2 (x).

5) (f (x)) ' = (6x^2 - 3) ' * (x + 2) + (x + 2) ' * (6x^2 - 3) = 12x * (x + 2) + 6x^2 - 3) = 16x^2 + 24x - 3.