Tentukan turunan dari f(x) = (x-2)^4 (x+2)²
Matematika
PranevaAnnisa
Pertanyaan
Tentukan turunan dari
f(x) = (x-2)^4 (x+2)²
f(x) = (x-2)^4 (x+2)²
1 Jawaban
-
1. Jawaban whongaliem
f(x) = (x - 2)^4 (x + 2)²
misal : u = (x - 2)^4 v = (x + 2)²
u' = 4 (x - 2)³ v' = 2 (x + 2)
soal dapat ditulis
f (x) = u.v
f'(x) = u'.v + u.v'
= 4 (x - 2)³ .(x + 2)² + (x - 2)^4 .2 (x + 2)
= 2 (x - 2)³ (x + 2) { 2 (x + 2) + x - 2 }
= 2 (x - 2)³ (x + 2) (2x + 4 + x - 2)
= 2 (x - 2)³ (x + 2) (3x + 2)