Найдите производную а) y=(1/x +8)(5x-2) б) у=(9- - вопрос №524542818529132 от Milasche4ka17 22.07.2022 01:57

Question

Алгебра: Найдите производную а) y=(1/x +8)(5x-2) б) у=(9- 1/х)(3х+2)

Milasche4ka17 · Answer

А) y=(1/x +8)(5x-2)
y` = (1/x +8)`(5x-2) + (1/x +8)(5x-2)` = (-1)/(x^2) * (5x-2) + (1/x +8)5 = -5/x + 2/(x^2) + 5/x + 40 = [(-5x) + (-2) + 10x]/2x^2 + 40 = 2/(x^2) + 40
Б) у=(9- 1/х)(3х+2)
у`=(9- 1/х)`(3х+2) + (9- 1/х)(3х+2)` = 1/(x^2) * (3х+2) + (9 - 1/x)3 = 3/x + 2/(x^2) + 27 - 3/x = 2/(x^2) + 27