1. The document is a math worksheet containing 5 calculus problems involving derivatives. 2. For each problem, the student set up the derivative using implicit differentiation and obtained the derivative expression. 3. The student provided the work and solutions for taking the derivatives of 5 functions: y = e(3x^2+7x), y = esin8x, y = (e^-6x - e^7x)^4, y = ln(6x^2 - 5), and y = 6(7x^2 + 9).

1. TUGAS PERBAIKAN NILAI MATEMATIKA
KUIS 2
TANGGAL 13 APRIL2015
NAMA : GERIAN DWIKISAKTISP
KELAS : 1 EA
SOAL!!
1. 𝑦 = 𝑒(3𝑥2+ 7𝑥)
2. 𝑦 = 𝑒sin8𝑥
3. 𝑦 = (𝑒−6𝑥 − 𝑒7𝑥)4
4. 𝑦 = (𝑛 (6𝑥2 − 5)
5. 𝑦 = 67𝑥2+ 5)
JAWABAN!!
1. 𝑦 = 𝑒(3𝑥2+ 7𝑥)
𝑚𝑖𝑠𝑎𝑙 𝑢 = 3𝑥2 + 7𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 6𝑥 + 7
𝑦 = 𝑒 𝑢 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 𝑒 𝑢 = 𝑒(3𝑥2+ 7𝑥)
→ 𝑦′ =
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 𝑒(3𝑥2+ 7𝑥) ∙ (6𝑥 + 7)
2. 𝑦 = 𝑒sin8𝑥
𝑚𝑖𝑠𝑎𝑙 𝑢 = sin 8𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 8cos 8𝑥
𝑦 = 𝑒 𝑢 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 𝑒 𝑢 = 𝑒sin8𝑥
→ 𝑦′ =
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 𝑒sin8𝑥 ∙ (8 cos 8𝑥)
𝑦′ = (8 cos 8𝑥) ∙ 𝑒sin8𝑥

2. 3. 𝑦 = (𝑒−6𝑥 − 𝑒7𝑥)4
𝑚𝑖𝑠𝑎𝑙 𝑢 = 𝑒−6𝑥 − 𝑒7𝑥 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= −6𝑒−6𝑥 − 7𝑒7𝑥
𝑦 = 𝑢4 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 4 𝑢3 = 4(𝑒−6𝑥 − 𝑒7𝑥)3
→ 𝑦 =
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 4(𝑒−6𝑥 − 𝑒7𝑥)3 ∙ (−6𝑒−6𝑥 − 7𝑒7𝑥)
𝑦′ = 4 (−6𝑒−6𝑥 − 7𝑒7𝑥) ∙ (𝑒−6𝑥 − 𝑒7𝑥)3
4. 𝑦 = 𝐼𝑛 (6𝑥2 − 5)
𝑚𝑖𝑠𝑎𝑙 𝑢 = 6𝑥2 − 5 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 12𝑥
𝑦 = 𝐼𝑛 𝑢 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
=
1
𝑢
=
1
6𝑥2− 5
→ 𝑦′ =
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
=
1
6𝑥2− 5
∙ 12𝑥
𝑦′ =
12𝑥
6𝑥2− 5
5. 𝑦 = 67 𝑥+9
𝑚𝑖𝑠𝑎𝑙 𝑢 = 7𝑥2 + 9 𝑚𝑎𝑘𝑎
𝑑𝑢
𝑑𝑥
= 14𝑥
𝑦 = 6 𝑢 𝑚𝑎𝑘𝑎
𝑑𝑦
𝑑𝑢
= 6 𝑢 ∙ 𝐼𝑛 6 = 67𝑥2=9
∙ 𝐼𝑛 6
→ 𝑦′ =
𝑑𝑦
𝑑𝑢
∙
𝑑𝑢
𝑑𝑥
= 67𝑥2+9
. 𝐼𝑛 6 .14𝑥
𝑦′ = 14𝑥 . 67𝑥2+9
. 𝐼𝑛 6