The document provides the solutions to 10 derivative problems involving various trigonometric and algebraic functions. It lists the functions and their derivatives, showing the work step-by-step in calculating each derivative. The solutions include taking the derivatives of sums, products, quotients, radicals, and composite functions involving trigonometric and exponential terms.

1. Nama :Miza Pisari
NPM : 0031417
Kelas : 1 Elektronika A
Tugas : MATEMATIKA
Carilah nilai turunan dari fungsi berikut ini.
1. 𝑦 = 𝑥7
+ 6𝑥5
+ 12𝑥3
2. 𝑦 = 𝑥−5
+ 2𝑥−3
+ 3𝑥−7
3. 𝑦 = √𝑥2 + √𝑥73
4. 𝑦 =
2
√ 𝑥
+
6
√𝑥3
5. 𝑦 = 𝑥2
.sin 2𝑥
6. 𝑦 = ( 𝑥2
+ 1). cos3𝑥
7. 𝑦 = sin 5𝑥 . tan 2𝑥
8. 𝑦 = cos3𝑥 . cot 4𝑥
9. 𝑦 =
sin 5𝑥
cos 7𝑥
10. 𝑦 =
cos 6𝑥
tan 2𝑥
Jawab:
1. 𝑦′
= 7𝑥6
+ 30𝑥4
+ 36𝑥2
2. 𝑦′
= −5𝑥−6
−6𝑥−4
−21𝑥−8
3. 𝑦 = 𝑥
2
2 + 𝑥
7
3 = 𝑥 + 𝑥
7
3
𝑦′
= 1 +
7
3
𝑥
7
3
−
3
3 = 1 +
7
3
𝑥
4
3
𝑦′ = 1 +
7
3
√ 𝑥43
4. 𝑦 =
2
𝑥
1
2
+
6
𝑥
3
2
= 2𝑥
−
1
2 + 6𝑥
−
3
2
𝑦′
= 2. −
1
2
. 𝑥
−
1
2
−
2
2 + 6. −
3
2
. 𝑥
−
3
2
−
2
2 = −𝑥
−
3
2−9𝑥
−
5
2 = −
1
𝑥
3
2
−
9
𝑥
5
2
𝑦′ = −
1
√𝑥3
−
9
√𝑥5
5. 𝑢 = 𝑥2
→ 𝑢′
= 2𝑥
𝑣 = sin 2𝑥 → 𝑣′
= 2. cos 𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= 2𝑥. sin 2𝑥 + 𝑥2
.2. cos 𝑥
𝑦′ = 2𝑥. sin2𝑥 + 2𝑥2
. cos 𝑥
6. 𝑢 = 𝑥2
+ 1 → 𝑢′
= 2𝑥
𝑣 = cos3𝑥 → 𝑣′
= −3. sin 3𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= 2𝑥. cos3𝑥 + ( 𝑥2
+ 1). −3. sin 3𝑥
𝑦′ = 2𝑥. cos3𝑥 + (−3𝑥2
− 3).sin 3𝑥
7. 𝑢 = sin 5𝑥 → 𝑢′
= 5. cos5𝑥
𝑣 = tan 2𝑥 → 𝑣′
= 2. 𝑠𝑒𝑐2
2𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= 5. cos5𝑥 . tan2𝑥 + sin 5𝑥 . 2. 𝑠𝑒𝑐2
2𝑥
𝑦′
= 5. cos5𝑥 .tan 2𝑥 + 2. sin 5𝑥 . 𝑠𝑒𝑐2
2𝑥
8. 𝑢 = cos3𝑥 → 𝑢′
= −3.sin 3𝑥
𝑣 = cot4𝑥 → 𝑣′
= −4. 𝑐𝑠𝑐2
4𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= −3. sin 3𝑥 . cot 4𝑥 + cos3𝑥 . −4. 𝑐𝑠𝑐2
4𝑥
𝑦′
= −3. sin 3𝑥 . cot 4𝑥 − 4. cos3𝑥 . 𝑐𝑠𝑐2
4𝑥
9. 𝑢 = sin 5𝑥 → 𝑢′
= 5. cos5𝑥
𝑣 = cos7𝑥 → 𝑣′
= −7. sin 7𝑥

2. 𝑦′
=
𝑢′
. 𝑣 − 𝑢. 𝑣′
𝑣2
=
5. cos5𝑥 . cos7𝑥 − sin 5𝑥 . −7. sin 7𝑥
(cos7𝑥)2
𝑦′
=
5. cos5𝑥 .cos 7𝑥 + 7. sin 5𝑥 . sin 7𝑥
𝑐𝑜𝑠27𝑥
10. 𝑢 = cos6𝑥 → 𝑢′
= −6.sin 6𝑥
𝑣 = tan 2𝑥 → 𝑣′
= 2. 𝑠𝑒𝑐2
2𝑥
𝑦′
=
𝑢′
. 𝑣 − 𝑢. 𝑣′
𝑣2
=
−6. sin 6𝑥. tan 2𝑥 − cos6𝑥.2. 𝑠𝑒𝑐2
2𝑥
(tan 2𝑥)2
𝑦′
=
−6. sin 6𝑥. tan2𝑥 − 2. cos6𝑥. 𝑠𝑒𝑐2
2𝑥
𝑡𝑎𝑛2 2𝑥