Jawaban:

a. f'(x) = (-8x - 6)/(2x² + 3x + 3)³

b. f'(x) = (-8 - 16x)(1 - x - x²)⁷

c. f'(x) = (-6x - 4)/3(-3x² - 4x + 5)^(2/3)

Penjelasan dengan langkah-langkah:

f(x) = u(x)^n → f'(x) = n{u'(x)}{u(x)}^(n-1)

Selain pakai rumus itu, bisa juga gunakan rule chain:

dy/dx = (dy/du) x (du/dv) x (dv/dx)

a. y = (2x² + 3x + 1)^-2

n = -2

u(x) = (2x² + 3x + 3)

u'(x) = 4x + 3

f'(x) = n{u'(x)}{u(x)}^(n-1)

f'(x) = (-2)(4x + 3)(2x² + 3x + 3)^-3

f'(x) = (-8x - 6)/(2x² + 3x + 3)³

b. y = (1 - x - x²)^8

n = 8

u(x) = (1 - x - x²)

u'(x) = (-1 - 2x)

f'(x) = n{u'(x)}{u(x)}^(n-1)

f'(x) = 8(-1 - 2x)(1 - x - x²)⁷

f'(x) = (-8 - 16x)(1 - x - x²)⁷

c. y = (-3x² - 4x + 5)^(1/3)

n = 1/3

u(x) = (-3x² - 4x + 5)

u'(x) = (-6x - 4)

f'(x) = n{u'(x)}{u(x)}^(n-1)

f'(x) = (-6x - 4)/3(-3x² - 4x + 5)^(2/3)