1. This document contains the work of a student named Barry Alkahfi in the 1st class of EA. It lists 10 derivative problems and shows the step-by-step work to find the derivatives of each function. 2. The functions include polynomials, radicals, trigonometric functions like sin, cos, and tan, and combinations of trig functions. 3. For each problem, the student correctly takes the derivative of the functions using derivative rules like the power rule, chain rule, product rule and quotient rule.

1. Matematika
Nama: Barry Alkahfi
Kelas : 1 EA
Tugas 1
Carilahturunandarinilaifungsiberikut!!!
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). cos 3𝑥
7. 𝑦 = sin 5𝑥 . tan 2𝑥
8. 𝑦 = cos 3𝑥 . cot 4𝑥
9. 𝑦 =
sin 5𝑥
cos 7𝑥
10. 𝑦 =
cos 6𝑥
tan 2𝑥
Jawaban
1. 𝑦′
= 7𝑥6
+ 30𝑥4
+ 36𝑥2
2. 𝑦′
= −5𝑥−6
−6𝑥−4
−21𝑥−8

2. 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
𝑦′−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. sin2𝑥 + 𝑥2
. 2.cos 𝑥
𝑦′ = 2𝑥. sin 2𝑥 + 2𝑥2
.cos 𝑥
6. 𝑢 = 𝑥2
+ 1 → 𝑢′
= 2𝑥
𝑣 = cos 3𝑥 → 𝑣′
= −3.sin 3𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= 2𝑥. cos 3𝑥 + ( 𝑥2
+ 1).−3. sin3𝑥
𝑦′ = 2𝑥. cos 3𝑥 + (−3𝑥2
− 3).sin 3𝑥
7. 𝑢 = sin 5𝑥 → 𝑢′
= 5.cos 5𝑥
𝑣 = tan 2𝑥 → 𝑣′
= 2. 𝑠𝑒𝑐2
2𝑥

3. 𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= 5.cos 5𝑥 . tan 2𝑥 + sin 5𝑥 . 2. 𝑠𝑒𝑐2
2𝑥
𝑦′
= 5.cos 5𝑥. tan 2𝑥 + 2. sin5𝑥 . 𝑠𝑒𝑐2
2𝑥
8. 𝑢 = cos 3𝑥 → 𝑢′
= −3. sin3𝑥
𝑣 = cot4𝑥 → 𝑣′
= −4. 𝑐𝑠𝑐2
4𝑥
𝑦′
= 𝑢′
. 𝑣 + 𝑢. 𝑣′
= −3.sin 3𝑥 . cot4𝑥 + cos 3𝑥 .−4. 𝑐𝑠𝑐2
4𝑥
𝑦′
= −3.sin 3𝑥 . cot4𝑥 − 4. cos 3𝑥 . 𝑐𝑠𝑐2
4𝑥
9. 𝑢 = sin 5𝑥 → 𝑢′
= 5.cos 5𝑥
𝑣 = cos 7𝑥 → 𝑣′
= −7.sin 7𝑥
𝑦′
=
𝑢′
. 𝑣 − 𝑢. 𝑣′
𝑣2
=
5.cos 5𝑥 . cos 7𝑥 − sin5𝑥 . −7.sin 7𝑥
(cos 7𝑥)2
𝑦′
=
5.cos 5𝑥. cos 7𝑥 + 7.sin 5𝑥 . sin7𝑥
𝑐𝑜𝑠27𝑥
10. 𝑢 = cos 6𝑥 → 𝑢′
= −6. sin6𝑥
𝑣 = tan 2𝑥 → 𝑣′
= 2. 𝑠𝑒𝑐2
2𝑥
𝑦′
=
𝑢′
. 𝑣 − 𝑢. 𝑣′
𝑣2
=
−6.sin 6𝑥. tan2𝑥 − cos 6𝑥. 2. 𝑠𝑒𝑐2
2𝑥
(tan 2𝑥)2
𝑦′
=
−6.sin 6𝑥. tan 2𝑥 − 2.cos 6𝑥. 𝑠𝑒𝑐2
2𝑥
𝑡𝑎𝑛22𝑥