Kuis 1 MTK

1. TUGAS PERBAIKAN NILAI MATEMATIKA
KUIS 1
TANGGAL : 27 MARET 2015
NAMA : GERIAN DWIKISAKTISANUSIPUTRA
SOAL!!
1. 𝑦 = (𝑥2 + 6𝑥)5 → 𝑦′ = ?
2. 𝑦 =
1
(𝑥3−6𝑥)4
→ 𝑦′ = ?
3. 𝑦 = √𝑥2 + 8𝑥
3
→ 𝑦′ = ?
4. 𝑦 = 6𝑥2 + 5𝑥 → 𝑦" = ?
5. 𝑦 = 7𝑥4 + sin 4𝑥 + cos 5𝑥 → 𝑦" = ?
JAWABAN!!
1. 𝑦 = (𝑥2 + 6𝑥)5
𝑚𝑖𝑠𝑎𝑙 4 = 𝑥2 + 6𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 2𝑥 + 6
𝑦 = 𝑢5 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 5𝑢4 = 5( 𝑥2 + 6𝑥)4
→
𝑑𝑢
𝑑𝑥
=
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 5 (𝑥2 + 6𝑥)4 ∙ (2𝑥 + 6)
= (10𝑥 + 30) ∙ (𝑥2 + 6𝑥)4
2. 𝑦 =
1
(𝑥3− 6𝑥)4
→ 𝑦 = (𝑥3 − 6𝑥)−4
𝑚𝑖𝑠𝑎𝑙 𝑢 = 𝑥3 − 6𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 3𝑥2 − 6
𝑦 = 𝑢−4 𝑚𝑎𝑘𝑎
𝜕𝑦
𝜕𝑢
= −4 𝑢−5 = −4 (𝑥3 − 6𝑥)−5
→
𝜕𝑦
𝜕𝑥
=
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= −4 (𝑥3 − 6𝑥)−5 ∙ (3𝑥2 − 6)

2. = (−12𝑥2 + 24) ∙ (𝑥3 − 6𝑥)−5 =
(−12𝑥2+ 24)
(𝑥3− 6𝑥)5
3. 𝑦 = √𝑥2 + 8𝑥
3
→ 𝑦 = (𝑥2 + 8𝑥)
1
3⁄
𝑚𝑖𝑠𝑎𝑙 𝑢 = 𝑥2 + 8𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 2𝑥 + 8
𝑦 = 𝑢
1
3⁄
𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 1
3⁄ 𝑢
−2
3⁄
= 1
3⁄ (𝑥2 + 8𝑥)
−2
3⁄
→
𝑑𝑦
𝑑𝑥
=
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 1
3⁄ (𝑥2 + 8𝑥)
−2
3⁄ ∙
∙ (2𝑥 + 8)
=
1
3⁄ (2𝑥+8)
(𝑥2+ 8𝑥)
2
3⁄
=
1
3⁄ (2𝑥+8)
√(𝑥2+ 8𝑥)23
4. 𝑦 = 6𝑥2 + 5𝑥
𝑦′ = 12𝑥 + 5
𝑦′′ = 12
5. 𝑦 = 7𝑥4 + sin 4𝑥 + cos5𝑥
𝑦′ = 28𝑥3 + (4 . cos 4𝑥) + (−5 . sin 5𝑥)
𝑦′ = 28𝑥3 + 4cos4𝑥 − 5 sin 5𝑥
𝑦′′ = 84𝑥2 + (−16 . sin 4𝑥) + (−25 .cos5𝑥)
𝑦′′ = 84𝑥2 − 16sin 4𝑥 − 25 cos5𝑥