F (x) = ln 3x-2/3x+2 y'' (x=1) = y = e^x/3x y' (x=-1) = y = 3^acrtgx/3 y' = f (x) = lnsin 3x/4 f' (x) =

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Математика

25 октября, 21:05

F (x) = ln 3x-2/3x+2 y'' (x=1) = y = e^x/3x y' (x=-1) = y = 3^acrtgx/3 y' = f (x) = lnsin 3x/4 f' (x) =

+3

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Мария Герасимова · Answer 1

1) (f (x)) ' = (ln ((3x - 2) / (3x + 2))) ' = (3x + 2) / (3x - 2).

(f (x)) '' = ((3x + 2) / (3x - 2)) ' = (3 * (3x - 2) - 3 * (3x + 2)) / (3x - 2) ^2 = - 12 / (3x - 2) ^2.

(f (1)) '' = - 12 / (3 - 2) ^2 = - 12.

2) y' = (e^x / 3x) ' = (e^x * 3x - 3 * e^x) / (3x) ^2 = e^x * (3x - 3) / (3x) ^2.

(y (-1)) ' = e^ (-1) * (3 * (-1) - 3) / (-3) ^2 = - 2/3 * e^ (-1).

3) (y) ' = (3 * arctg (x/3)) ' = 3 * 1/3 * 1 / (1 + (x/3) ^2 = 1 / (1 + (x/3) ^2.

4) y' = (ln (sin (3/4x)) ' = 1/sin (3/4x) * cos (3/4x) * 3/4 = 3/4ctg (3/4x).