tugas mtk kelompok 3

1. KELOMPOK 3
“TURUNAN”
1 EB
DI SUSUN OLEH:
1. BAYU FIRDAUS
2. M. TEDDY KANTORI
3. PRADANA .P.S
4. ZALDI SUGIANTO

2. EXERCISE
4.1
1. 𝑓 𝑥 = 4
2. 𝑓 𝑥 = 7𝑥 + 2
3. 𝑓 𝑥 = −3𝑥 − 9
4. 𝑓 𝑥 = 10 − 3𝑥
5. 𝑓 𝑥 = −
3
4
𝑥
6. 𝑓 𝑥 = 5𝑥2
+ 𝑥 − 3
7. 𝑓 𝑥 = 𝑥3
+ 13𝑥
8. 𝑓 𝑥 = 2𝑥3
+ 15
9. 𝑓 𝑥 = −
1
𝑥
10. 𝑓 𝑥 =
1
𝑥
ANSWER:
4.1
1. 𝑓 𝑥 = 4
𝑓1
𝑥 = 0
2. 𝑓 𝑥 = 7𝑥 + 2
𝑓1
𝑥 = 7
3. 𝑓𝑥 = −3 − 9
𝑓1
𝑥 = −3
4. 𝑓 𝑥 = 10 − 3𝑥
𝑓1
𝑥 = −3
5. 𝑓 𝑥 = −
3
4
𝑥
𝑓1
𝑥 = −
3
4
6. 𝑓 𝑥 = 5𝑥2
+ 𝑥 − 3
𝑓1
𝑥 = 10𝑥 + 1
7. 𝑓 𝑥 = 𝑥3
+ 13𝑥
𝑓1
𝑥 = 2𝑥 + 13
8. 𝑓 𝑥 = 2𝑥3
+ 15
𝑓1
𝑥 = 6𝑥2
9. 𝑓 𝑥 = −
1
𝑥
= −1. 𝑥−1
𝑓1
𝑥 = 1. 𝑥−2
=
1
𝑥2
10. 𝑓 𝑥 =
1
𝑥
= 1. 𝑥−
1
2
𝑓1
𝑥 = −
1
2
. 𝑥−
3
2
𝑓1
𝑥 =
−
1
2
𝑥3

3. Exercise
4.1
1. 𝑓 𝑥 = 7
2. 𝑦 = 5
3. 𝑓 𝑥 = 0
4. 𝑓 𝑡 = −3
5. 𝑓 𝑥 = 𝜋
6. 𝑔 𝑥 = 25
7. 𝑠 𝑡 = 100
8. 𝑧 𝑥 = 23
9. 𝑦 = −
1
2
10. 𝑓 𝑥 = 41
ANSWER
4.1
1. 𝑓 𝑥 = 7
𝑓1
𝑥 = 0
2. 𝑦 = 5
𝑦1
= 0
3. 𝑓𝑥) = 0
𝑓1
𝑥 = 0
4. 𝑓 𝑡 = −3
𝑓1
𝑡 = 0
5. 𝑓 𝑥 = 𝜋
𝑓1
𝑥 =
6. 9 𝑥 = 25
𝑔1
𝑥 = 0
7. 𝑠 𝑡 = 100
𝑠1
𝑡 = 0
8. 𝑧 𝑥 = 23
𝑧1
𝑥 = 62
9. 𝑦 = −
1
2
𝑦1
= 0
10. 𝑓 𝑥 = 41
−1 𝑥 = 0

4. Exercise
4.3
1. 𝑓 𝑥 = 9𝑥
2. 𝑔 𝑥 = −75𝑥
3. 𝑓 𝑥 = 𝑥 + 1
4. 𝑦 = 50𝑥 + 30
5. 𝑓 𝑡 = 2𝑡 + 5
6. 𝑓 𝑥 = 𝜋𝑥 − 25
7. 𝑓 𝑥 = −
3
4
𝑥
8. 𝑠 𝑡 = 100𝑡 − 45
9. 𝑧 𝑥 = 0.08𝑥 + 400
10. 𝑓 𝑥 = 41𝑥 + 1
ANSWER
4.3
1. 𝑓 𝑥 = 9𝑥
𝑓1
𝑥 = 9
2. 𝑔 𝑥 = −75𝑥
𝑔1
𝑥 = −75
3. 𝑓 𝑥 = 𝑥 + 1
𝑓1
𝑥 = 1
4. 𝑦 = 50𝑥 + 30
𝑦1
= 50
5. 𝑓 𝑡 = 2𝑡 + 5
𝑓1
𝑡 = 2
6. 𝑓 𝑥 = 𝜋𝑥 − 25
𝑓1
𝑥 =
7. 𝑓 𝑥 = −
3
4
𝑥
𝑓1
𝑥 = −
3
4
8. 𝑠 𝑡 = 100𝑡 − 45
𝑠1
𝑡 = 100
9. 𝑧 𝑥 = 0.08𝑥 + 400
𝑧1
𝑥 = 0.08
10. 𝑓 𝑥 = 41𝑥 + 1
= 41𝑥
1
2 + 1
𝑓1
𝑥 =
1
2
. 41. 𝑥−
1
2
𝑓1
𝑥 =
4
1
2
𝑥

5. EXERCISE
4.4
1. 𝑓 𝑥 = 𝑥3
2. 𝑔 𝑥 = 𝑥100
3. 𝑓 𝑥 = 𝑥
1
4
4. 𝑦 = 𝑥
5. 𝑓 𝑡 = 𝑡1
6. 𝑓 𝑥 = 𝑥 𝜋
7. 𝑓 𝑥 =
1
𝑥5
8. 𝑠 𝑡 = 𝑡0.6
9. 𝑕 𝑠 = 𝑠
4
5
10. 𝑓 𝑥 =
1
𝑥23
ANSWER
4.4
1. 𝑓 𝑥 = 𝑥3
𝑓1
𝑥 = 3𝑥2
2. 𝑔 𝑥 = 𝑥100
𝑔1
𝑥 = 100𝑥99
3. 𝑓 𝑥 = 𝑥
1
4
𝑓1
𝑥 =
1
4
𝑥−
3
4
4. 𝑦 = 𝑥
𝑦 = 𝑥
1
2=𝑦1
𝑥 =
1
2
𝑥−
1
2
5. 𝑓 𝑡 = 𝑡1
𝑓1
𝑡 = 3𝑡2
6. 𝑓 𝑥 = 𝑥 𝜋
𝑓1
(𝑥)=
7. 𝑓 𝑥 =
1
𝑥5
𝑓 𝑥 = 𝑥−5
= 𝑓1
𝑥 = −5𝑥−6
8. 𝑠 𝑡 = 𝑡0.6
𝑠1
𝑥 = 0.6𝑡−0.4
9. 𝑕 𝑠 = 𝑠
4
5
𝑕1
𝑠 =
4
5
𝑠−
1
5
10. 𝑓 𝑥 =
1
𝑥23
𝑓 𝑥 = 𝑥−
2
3 = 𝑓1
𝑥 = −
2
3
𝑥−
5
3

6. Exercise
4.5
1. If 𝑓 𝑥 = 𝑥3
, find 𝑓′
5 .
2. If 𝑔 𝑥 = −100, find 𝑔′
(25).
3. If 𝑓 𝑥 = 𝑥
1
4, find 𝑓′
81 .
4. If 𝑦 = 𝑥, find
𝑑𝑦
𝑑𝑥 𝑥=49
5. If 𝑓 𝑡 = t, find 𝑓′
(19)
6. If 𝑓 𝑥 = 𝑥 𝜋
, find 𝑓′
(10)
7. If 𝑓 𝑥 =
1
𝑥5
, find 𝑓′
(2)
8. If 𝑠 𝑡 = 𝑡0.6
, find 𝑠′
(32)
9. If 𝑓 𝑠 = 𝑠
4
5, find 𝑕′
(32)
10. If 𝑦 =
1
𝑥23 , find
dy
dx 64
ANSWER
4.5
1. If𝑓 𝑥 = 𝑥3
, find 𝑓′
(5)
for 𝑓1
𝑥 = 𝑥3
𝑓1
𝑥 = 3𝑥2
𝑓1
5 = 3 5 2
= 75
2. If 𝑔 𝑥 = −100, find 𝑔′
25
for 𝑔 𝑥 = −100
𝑔1
𝑥 = 0
𝑔1
25 = 0
3. If 𝑓 𝑥 = 𝑥
1
4
,
find 𝑓′
(81)
for 𝑓 𝑥 = 𝑥
1
4
𝑓1
𝑥 =
1
4
𝑥−
3
4
𝑓1
81 =
1
4
81 −
3
4
=
4. 𝐼𝑓 𝑦 = 𝑥, 𝑓𝑖𝑛𝑑
𝑑𝑦
𝑑𝑥 𝑥=49
𝑓𝑜𝑟 𝑦 𝑥 = 𝑥 = 𝑥
1
2
𝑦1
49 =
𝑑𝑦
𝑑𝑥
=
1
2
𝑥−
1
2
𝑦1
49 =
1
2
(49)−
1
2
5. If f(t)=t, find f’(19)
𝑓𝑜𝑟 𝑓 𝑡 = 𝑡
F’(t)=1
f’ (19)=1
6. 𝐼𝑓 𝑓 𝑥 = 𝑥 𝜋
, 𝑓𝑖𝑛𝑑 𝑓′
10
𝐹𝑜𝑟 𝑓 𝑥 = 𝑥 𝜋
7. 𝐼𝑓𝑛𝑓 𝑥 =
1
𝑥5
, 𝑓𝑖𝑛𝑑 𝑓′
2
𝐹𝑜𝑟 𝑓 𝑥 =
1
𝑥5
= 𝑥−5
𝑓′
𝑥 = −5𝑥−6
𝑓′
2 = −5𝑥−6
=
8. 𝐼𝑓 𝑠 𝑡 = 𝑡0.6
, 𝑓𝑖𝑛𝑑 𝑠′
32
𝐹𝑜𝑟 𝑠 𝑡 = 𝑓0.6
𝑠′
𝑡 = 0.6𝑡−0.4
𝑠′
32 = 0.6 32 −0.4
=

7. 9. 𝐼𝑓 𝑕 𝑠 = 𝑠
4
5, 𝑓𝑖𝑛𝑑 𝑕′
32
𝐹𝑜𝑟 𝑕 𝑠 = 𝑠
4
5
𝑕′
𝑠 =
4
5
𝑠−
1
3
𝑕′
32 =
4
5
(32)−
1
5
=
10. 𝐼𝑓 =
1
𝑥23 , 𝑓𝑖𝑛𝑑
𝑑𝑦
𝑑𝑥 64
𝑦 =
1
𝑥23 = 𝑥−
2
3
𝑦1
= −
2
3
𝑥 −
3
3
Type equation here.

8. EXERCISE
5.1
1. 𝑓 𝑥 = 2𝑥3
2. 𝑔 𝑥 =
𝑥100
25
3. 𝑓 𝑥 = 20𝑥
1
4
4. 𝑦 = −16 𝑥
5. 𝑓 𝑡 =
2𝑡
3
6. 𝑓 𝑥 =
𝑥 𝜋
2𝜋
7. 𝑓 𝑥 =
10
𝑥5
8. 𝑠 𝑡 = 100𝑡
4
5
9. 𝑕 𝑠 = −25𝑠
4
5
10. 𝑓 𝑥 =
1
4 𝑥23
ANSWER
5.1
1. 𝑓 𝑥 = 2𝑥3
𝑓1
𝑥 = 6𝑥2
2. 𝑔 𝑥 =
𝑥100
25
𝑔 𝑥 =
100 𝑥
25
= 4𝑥99
3. 𝑓 𝑥 = 20𝑥
1
4
𝑓1
𝑥 = 5𝑥−
3
4
4. 𝑦 = −16 𝑥
𝑦 = −16𝑥
1
2 = 𝑦1
= −8𝑥−
1
2
5. 𝑓 𝑡 =
2𝑡
3
𝑓1
𝑡 =
2
3
6. 𝑓 𝑥 =
𝑥 𝜋
2𝜋
7. 𝑓 𝑥 =
10
𝑥5
𝑓 𝑥 = 10𝑥−5
= 𝑓1
𝑥
= −50𝑥−6
8. 𝑠 𝑡 = 100𝑡0.6
𝑠1
𝑡 = 60𝑥−0.4
9. 𝑕 𝑠 = −25𝑠
4
5
𝑕1
𝑠 = −20𝑠−
1
5
10. 𝑓 𝑥 =
1
4 𝑥23
𝑓 𝑥 =
1
4
𝑥−
2
3
𝑓1
𝑥 = −
2
12
𝑥 −
5
3
= −
1
6
𝑥 −
5
3