a) f (x) = (8x^5-5x^8) ^12

б) f (X) = (1/9 - 3x³) ^27

в) f (x) = (4x^10-5x) ^10

г) f (x) = (x^5-4x^4) ^130

Вычислите производные функций

ответы

б) - 81x² (1/9-3x³) ^26

г) 130x³ (5x-16) (x^5-4x^4) ^129

a) f (x) = (8x⁵-5x⁸) ¹²

f ' (x) = ((8x⁵-5x⁸) ¹²) ' = 12 * (8x⁵-5x⁸) ¹¹ * (8x⁵-5x⁸) ' = 12 * (8x⁵-5x⁸) ¹¹ * (40x⁴-40x⁷) = 12 * (8x⁵-5x⁸) ¹¹ * 40x⁴ (1-x³) = 480x⁴ * (8x⁵-5x⁸) ¹¹ * (1-x³)

б) f (X) = (1/9 - 3x³) ²⁷

f ' (x) = ((1/9 - 3x³) ²⁷) ' = 27 (1/9 - 3x³) ²⁶ * (1/9 - 3x³) ' = 27 (1/9 - 3x³) ²⁶ * (-3*3x²) = 27 (1/9 - 3x³) ²⁶ * (-9x²) = - 243x² * (1/9 - 3x³) ²⁶

в) f (x) = (4x¹⁰-5x) ¹⁰

f ' (x) = ((4x¹⁰-5x) ¹⁰) ' = 10 (4x¹⁰-5x) ⁹ * (4x¹⁰-5x) ' = 10 (4x¹⁰-5x) ⁹ * (40x⁹-5) = 10 (4x¹⁰-5x) ⁹ * 5 (8x⁹-1) = 50 (4x¹⁰-5x) ⁹ * (8x⁹-1)

г) f (x) = (x⁵-4x⁴) ¹³⁰

f ' (x) = ((x⁵-4x⁴) ¹³⁰) ' = 130 (x⁵-4x⁴) ¹²⁹ * (x⁵-4x⁴) ' = 130 (x⁵-4x⁴) ¹²⁹ * (5x⁴-16x³) = 130 (x⁵-4x⁴) ¹²⁹ * x³ (5x-16) = 130*x³ * (x⁵-4x⁴) ¹²⁹ * (5x-16)

a) f (x) = (8x⁵-5x⁸) ¹²

f ' (x) = 12 (8x⁵-5x⁸) ¹¹ * (40x⁴-40x⁷)

б) f (X) = (1/9 - 3x³) ²⁷ ваш ответ не верный

f ' (x) = 27 (1/9-3x³) ²⁶ * (-9x²) = - 243x² (1/9-3x³) ²⁶

в) f (x) = (4x^10-5x) ^10

f ' (x) = 10 (4x¹⁰-5x) 9 * (40x⁹-5)

г) f (x) = (x^5-4x^4) ^130

f ' (x) = 130 (x⁵-4x⁴) ¹²⁹ * (5x⁴-16x³)