Matematika Carilah turunan pertama dari fungsi f(x) = (3x + 2)(2x + 4) ! *

monarohanulv – March 08, 2023

Carilah turunan pertama dari fungsi f(x) = (3x + 2)(2x + 4) ! *

TURUNAN ALJABAR

• y = xⁿ = → y' = n.xⁿ⁻¹
• y = x → y' = 1
• y = c → y' = 0

Sifat turunan

1. y = u.v → y' = u'v + uv'
2. y = u/v → y' = (u'v – uv') / v²

SOAL

f(x) = (3x + 2)(2x + 4)

f(x) = 6x² + 12x + 4x + 8

f(x) = 6x² + 16x + 8

f'(x) = 2(6x)²⁻¹ + 1(16x)¹⁻¹ + 0

= 12x¹ + 16x⁰

= 12x + 16

cara lain

f(x) = (3x + 2)(2x + 4)

u v

u = (3x + 2) → u' = 1(3x)¹⁻¹ = 3x⁰ = 3

v = (2x + 4) → v' = 1(2x)¹⁻¹ = 2x⁰ = 2

sifat : y = u . v → y' = u'v + uv'

maka:

f(x) = (3x + 2)(2x + 4)

f'(x) = [3 . (2x + 4)] + [(3x + 2) . 2]

f'(x) = [6x + 12] + [6x + 4]

= 12x + 16

Penjelasan dengan langkah-langkah:

f(x) = (3x + 2)(2x + 4)

f(x) = 6x² + 16x + 8

f'(x) = 6.2x²-¹ + 16 + 0

f'(x) = 12x + 16

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