Find the derivative of the following functions: 1) y = (14x + 2)⁶ 2) y = (17 - 5x² + 6x)⁴ 3) y = 16(2x - 7)³ 4) y = 1 / (9x + 1)⁴ 5) y = 3 / (3 - 4x)⁶ 6) y = 2√(7x + 11) 7) y = √(x/2) - 3 8) y = sin(6x - π/4) 9) y = 6cos(2x + π) 10) y = tg(9x - π/3) 11) y = 7ctg(x/5 + π/2) 12) y = 3sin²(4x + π/6)

y = (14x + 2)⁶

Используем правило цепочки: y' = 6(14x + 2)⁵ * 14

y' = 84(14x + 2)⁵

Ответ: y' = 84(14x + 2)⁵

y = (17 - 5x² + 6x)⁴

Используем правило цепочки: y' = 4(17 - 5x² + 6x)³ * (-10x + 6)

y' = (24 - 40x)(17 - 5x² + 6x)³

Ответ: y' = (24 - 40x)(17 - 5x² + 6x)³

y = 16(2x - 7)³

y' = 16 * 3(2x - 7)² * 2

y' = 96(2x - 7)²

Ответ: y' = 96(2x - 7)²

y = 1 / (9x + 1)⁴ = (9x + 1)⁻⁴

y' = -4(9x + 1)⁻⁵ * 9

y' = -36 / (9x + 1)⁵

Ответ: y' = -36 / (9x + 1)⁵

y = 3 / (3 - 4x)⁶ = 3(3 - 4x)⁻⁶

y' = 3 * (-6)(3 - 4x)⁻⁷ * (-4)

y' = 72 / (3 - 4x)⁷

Ответ: y' = 72 / (3 - 4x)⁷

y = 2√(7x + 11) = 2(7x + 11)^(1/2)

y' = 2 * (1/2) * (7x + 11)^(-1/2) * 7

y' = 7 / √(7x + 11)

Ответ: y' = 7 / √(7x + 11)

y = √(x/2) - 3 = (x/2)^(1/2) - 3

y' = (1/2)(x/2)^(-1/2) * (1/2)

y' = 1 / (4√(x/2)) = 1 / (2√2√x) = √2 / (4√x)

Ответ: y' = √2 / (4√x)

y = sin(6x - π/4)

y' = cos(6x - π/4) * 6

y' = 6cos(6x - π/4)

Ответ: y' = 6cos(6x - π/4)

y = 6cos(2x + π)

y' = 6 * (-sin(2x + π)) * 2

y' = -12sin(2x + π)

Ответ: y' = -12sin(2x + π)

y = tg(9x - π/3)

y' = (1 / cos²(9x - π/3)) * 9

y' = 9 / cos²(9x - π/3)

Ответ: y' = 9 / cos²(9x - π/3)

y = 7ctg(x/5 + π/2)

y' = 7 * (-1 / sin²(x/5 + π/2)) * (1/5)

y' = -7 / (5sin²(x/5 + π/2))

Ответ: y' = -7 / (5sin²(x/5 + π/2))

y = 3sin²(4x + π/6)

y' = 3 * 2sin(4x + π/6) * cos(4x + π/6) * 4

y' = 24sin(4x + π/6)cos(4x + π/6) = 12sin(8x + π/3)

Ответ: y' = 12sin(8x + π/3)