Найти производную функции? 1) y=3+2x-3x^2+5x^3 2) y=(7x-2)*x^2 3) x*e^x 4) y+2sinx+1/3cosx 5) y3ctgx-4tgx 6) y=3 arcsinx-5arccosx

Найдем производную функции: y = 3 + 2x - 3x^2 + 5x^3.

y’ = (3 + 2x - 3x^2 + 5x^3)’ = 0 + 2 * 1 – 3 * 2x + 5 * 3x^2 = 15x^2 – 6x + 2.

Найдем производную функции: y = (7x - 2) * x^2.

y’ = ((7x - 2) * x^2)’ = (7x - 2)’ * x^2 + (7x - 2) * (x^2)’ = 7 * x^2 + (7x – 2) * 2x = 7x^2 + 14x^2 – 4x = 21x^2 – 4x.

Найдем производную функции: y = x * e^x.

y’ = (x * e^x)’ = x’ * e^x + x * (e^x)’ = 1 * e^x + x * e^x = e^x + xe^x.

Найдем производную функции: y = 2sin x + 1/(3cos x).

y’ = (2sin x + 1/(3cos x))’ = 2cos x – 1 / ((3cos x)^2) * (-3 sin x) = 2cos x + 3 sin x / (9cos^2 x).

Найдем производную функции: y = 3ctg x - 4tg x.

y’ = (3ctg x - 4tg x)’ = -3/(sin^2 x) – 4/(cos^2 x) = (-3 cos^2 x - 4 sin^2 x) / ((sin^2 x) (cos^2 x)) = - (3 cos^2 x + 3 sin^2 x + sin^2 x) / ((sin^2 x) (cos^2 x)) = - (3 + sin^2 x) / ((sin^2 x) (cos^2 x)).

Найдем производную функции: y = 3 arcsin x – 5 arccos x.

y’ = (3 arcsin x – 5 arccos x)’ = 3 / √(1 – x^2) + 5 / √(1 – x^2) = 8 / √(1 – x^2).

Найдем производную функции: y = ln x / x.

y’ = (ln x / x)’ = (1/x * x – 1 * ln x) / (x^2) = (1 – ln x) / (x^2).

Найдем производную функции: y = (4 - 5x) / (4 + 5x).

y’ = ((4 - 5x) / (4 + 5x))’ = ((4 - 5x)’ * (4 + 5x) - (4 + 5x)’ * (4 - 5x)) / (4 + 5x)^2 = (- 5 * (4 + 5x) - 5 * (4 - 5x)) / (4 + 5x)^2 = (- 20 – 25x – 20 + 25x) / (4 + 5x)^2 = -40 / (4 + 5x)^2.