tugas kalkulus

1. TUGAS MATEMATIKA KALKULUS
HALAMAN 33 - 44
Disusun Oleh :
Nama : 1. Barry Alkhafi
2. AchmadTrybuana Kurniasandy
3. AuliaRamadhani
4.Faizal
Kelas : 1 EA
Semester : 2 ( DUA )
POLITEKNIK MANUFAKTUR NEGERI BANGKA BELITUNG
2014/2015
Kawasan Industri Air Kantung, Sungailiat-Bangka 33211
Telp : 0717-93586, 95252 Faks : 0717-93585
E-mail : polman@polman-babel.ac.id
Website : http://polman-babel.ac.id

2. “ HALAMAN 33-40 “
Jawaban :
1. f(x) = 20ex
fꞌ(x) = 20.
𝒅
𝒅𝒙
(ex)
= 20ex
2. y = e3x
yꞌ(x) = e3x.
𝒅
𝒅𝒙
(5x3)
= 𝒆 𝟓𝒙 𝟑
(15x2)
= 15x2 𝒆 𝟓𝒙 𝟑
3. g(x) = 𝒆 𝟓𝒙 𝟑
gꞌ(x) = 𝒆 𝟓𝒙 𝟑
(.
𝒅
𝒅𝒙
(5x3)
= 𝒆 𝟓𝒙 𝟑
( (15x2)
= 15x2 𝒆 𝟓𝒙 𝟑
4. y = -4𝒆 𝟓𝒙 𝟑
yꞌ= -4.
𝒅
𝒅𝒙
(𝒆 𝟓𝒙 𝟑
)
= -4.𝒆 𝟓𝒙 𝟑
.
𝒅
𝒅𝒙
(5x3)
= -4.𝒆 𝟓𝒙 𝟑
(15x2)
= -60x2 𝒆 𝟓𝒙 𝟑
Temukan turunan dari fungsi yang diberikan
1. f(x) = 20ex 6. f(x) = 15x2 +10ex
2. y = e3x
7. g(x) = 𝒆 𝟕𝒙−𝟐𝒙 𝟑
3. g(x) = 𝒆 𝟓𝒙 𝟑
8. f(t) =
𝟏𝟎𝟎
𝒆−𝟎.𝟓𝒕
4. y = -4𝒆 𝟓𝒙 𝟑
9. g(t) = 2500e2t+1
5. h(x) = 𝒆−𝟏𝟎𝒙 𝟑
10. f(x) =
𝟏
√𝟐𝝅
𝒆
𝒙 𝟐
𝟐

3. 5. h(x) = 𝒆−𝟏𝟎𝒙 𝟑
hꞌ(x) = 𝒆−𝟏𝟎𝒙 𝟑
.
𝒅
𝒅𝒙
(-10x3)
= 𝒆−𝟏𝟎𝒙 𝟑
(-30x2)
= -30x2 𝒆−𝟏𝟎𝒙 𝟑
6. f(x) = 15x2 + 10ex
fꞌ(x) = 15x2 + 10.
𝒅
𝒅𝒙
(ex)
= 30x + 10ex
7. g(x) = 𝒆 𝟕𝒙−𝟐𝒙 𝟑
gꞌ(x) = 𝒆 𝟕𝒙−𝟐𝒙 𝟑
.
𝒅
𝒅𝒙
(7x-2x3)
= 𝒆 𝟕𝒙−𝟐𝒙 𝟑
(7-6x)
= 7-6x𝒆 𝟕𝒙−𝟐𝒙 𝟑
8. f(t) =
𝟏𝟎𝟎
𝐞−𝟎.𝟓𝒕
fꞌ(t) = 100.e0.5t
= 100. e0.5t.
𝒅
𝒅𝒙
(0.5t)
= 100. e0.5t(0.5)
= 50e0.5t
9. g(t) = 2500e2t+1
gꞌ(t) = 2500e2t+1.
𝒅
𝒅𝒙
(2t+1)
= 2500e2t+1.(2)
= 5000e2t+1
10. f(x) =
𝟏
√𝟐𝝅
e
𝒙𝟐
𝟐
fꞌ(x) =
𝟏
√𝟐𝝅
.e
𝟏
𝟐
x2.
𝒅
𝒅𝒙
(
𝟏
𝟐
x2)
=
𝟏
√𝟐𝝅
.e
𝟏
𝟐
x2.(x)
=
𝒙
√𝟐𝝅
.e
𝟏
𝟐
x2

4. Jawaban :
1. f(x) = 20 ln x
fꞌ(x) = 20 .
𝒅
𝒅𝒙
(ln x)
= 20.
𝟏
𝒙
=
𝟐𝟎
𝒙
2. y = ln 3x
yꞌ =
𝟏
𝟑𝒙
.
𝒅
𝒅𝒙
(3x)
=
𝟏
𝟑𝒙
. (3x)
=
𝟏
𝒙
3. g(x) = ln(5x3)
gꞌ(x) =
𝟏
𝟓𝒙 𝟑 .
𝒅
𝒅𝒙
(5x3)
=
𝟏
𝟓𝒙 𝟑.(15x2)
=
𝟑
𝒙
4. y = - 4 ln (5x3)
yꞌ = - 4.
𝟏
𝟓𝒙 𝟑.
𝒅
𝒅𝒙
(5x3)
= - 4.
𝟏
𝟓𝒙 𝟑.(15x2)
= -4.
𝟑
𝒙
= -
𝟏𝟐
𝒙
Temukan turunan dari fungsi yang diberikan
1. f(x) = 20 ln x 6. f(x) = 15x2 + 10ln x
2. y = ln 3x 7. g(x) = ln(7x-2x3)
3. g(x) = ln(5x3) 8. f(t) = ln(3t2 + 5t – 20)
4. y = -4 ln (5x3) 9. g(t) = ln(et)
5. h(x) = ln(-10x3) 10. f(x) = ln(ln x)

5. 5. h(x) = ln(-10x3)
hꞌ(x) =
𝟏
−𝟏𝟎𝒙 𝟑 .
𝒅
𝒅𝒙
(-10x3)
=
𝟏
−𝟏𝟎𝒙 𝟑(-30x2)
=
𝟑
𝒙
6. f(x) = 15x2 + 10ln x
fꞌ(x) = 15x2 + 10.
𝒅
𝒅𝒙
(ln x)
= 30x + 10.
𝟏
𝒙
= 30x +
𝟏𝟎
𝒙
7. g(x) = ln(7x-2x3)
gꞌ(x) =
𝟏
𝟕𝒙−𝟐𝒙 𝟑.
𝒅
𝒅𝒙
(7x-2x3)
=
𝟏
𝟕𝒙−𝟐𝒙 𝟑. (7x-2x3)
=
𝟕−𝟔𝒙 𝟐
𝟕𝒙−𝟐𝒙 𝟑
8. f(t) = ln(3t2 + 5t – 20)
fꞌ(t) =
𝟏
𝟑𝒕 𝟐+𝟓𝒕−𝟐𝟎
.
𝒅
𝒅𝒙
(𝟑𝒕 𝟐
+ 𝟓𝒕 − 𝟐𝟎)
=
𝟏
𝟑𝒕 𝟐+𝟓𝒕−𝟐𝟎
. ( 𝟔𝒕+ 𝟓)
=
𝟔𝒕+𝟓
𝟑𝒕 𝟐+𝟓𝒕−𝟐𝟎
9. g(t) = ln(et)
gꞌ(t) =
𝟏
𝒆 𝒕 .
𝒅
𝒅𝒙
(et)
=
𝟏
𝒆 𝒕(e)
=
𝒆
𝒆 𝒕
10. f(x) = ln(ln x)
fꞌ(x) =
𝟏
𝐥𝐧 𝒙
.
𝒅
𝒅𝒙
(ln x)
=
𝟏
𝐥𝐧 𝒙
. (
𝟏
𝒙
)
=
𝟏
𝐥𝐧 𝒙.𝒙

6. Jawaban :
1. f(x) = 20 (3x)
fꞌ(x) = 20.
𝒅
𝒅𝒙
(3x)
= 20(ln3)3x
2. y = 53x
yꞌ = (ln 5)53x.
𝒅
𝒅𝒙
(3x)
= (ln 5)53x.(3)
= 3(ln 5)53x
3. g(x) = 𝟐 𝟓𝐱 𝟑
gꞌ(x) = (ln 2)𝟐 𝟓𝐱 𝟑
.
𝒅
𝒅𝒙
(5x3)
= (ln 2)𝟐 𝟓𝐱 𝟑
(15x2)
= 15x2(ln 2) 𝟐 𝟓𝐱 𝟑
4. y = -4(𝟐 𝟓𝐱 𝟑
)
yꞌ = -4.
𝒅
𝒅𝒙
(𝟐 𝟓𝐱 𝟑
)
= -4(ln 2)𝟐 𝟓𝐱 𝟑
.(15x2)
= -60x2(ln 2)𝟐 𝟓𝐱 𝟑
Temukanturunan dari fungsi yang diberikan
1. f(x) = 20 (3x) 6. f(x) = 15x2 + 10(5x3)
2. y = 53x
7. g(x) = 𝟑 𝟕𝒙−𝟐𝒙 𝟑
3. g(x) = 𝟐 𝟓𝒙 𝟑
8. f(t) =
𝟏𝟎𝟎
𝟏𝟎−𝟎.𝟓𝒕
4. y = -4( 𝟐 𝟓𝒙 𝟑
) 9. g(t) = 2500(52t+1)
5. h(x) = 𝟒−𝟏𝟎𝒙 𝟑
10. f(x) = 8
𝒙 𝟐
𝟐

7. 5. h(x) = 𝟒−𝟏𝟎𝐱 𝟑
hꞌ(x) = (ln 4)𝟒−𝟏𝟎𝐱 𝟑
.
𝒅
𝒅𝒙
(-30x2)
= (ln 4)𝟒−𝟏𝟎𝐱 𝟑
. (-30x2)
= -30x2(ln 4)𝟒−𝟏𝟎𝐱 𝟑
6. f(x) = 15x2 + 10(5x3)
fꞌ(x) = 15x2 + 10.
𝒅
𝒅𝒙
(53x)
= 30x + 10(ln 5)53.3
= 30x + 30(ln 5)53
7. g(x) = 𝟑 𝟕𝐱−𝟐𝐱 𝟑
gꞌ(x) = (ln 3)𝟑 𝟕𝐱−𝟐𝐱 𝟑
.
𝒅
𝒅𝒙
(7x-2x3)
= (ln 3)𝟑 𝟕𝐱−𝟐𝐱 𝟑
.(7-6x2)
= 7-6x2(ln 3)𝟑 𝟕𝐱−𝟐𝐱 𝟑
8. f(t) =
𝟏𝟎𝟎
𝟏𝟎−𝟎.𝟓𝒕
fꞌ(t) = 100. 100.5t
= 100.(ln 10)100.5t.
𝒅
𝒅𝒙
(0.5t)
= 100.(ln 10)100.5t. 0.5
= 50(ln 10)100.5t
9. g(t) = 2500(52t+1)
gꞌ(t) = 2500.
𝒅
𝒅𝒙
(52t+1)
= 2500(ln 5)52t+1.
𝒅
𝒅𝒙
(2t+1)
= 2500(ln 5)52t+1.2
= 5000(ln 5)52t+1

8. 10. f(x) = 8
𝒙 𝟐
𝟐
= 8−
𝟏
𝟐
x2
fꞌ(x) = (ln 8)8−
𝟏
𝟐
x2.
𝒅
𝒅𝒙
(−
𝟏
𝟐
x2)
= (ln 8)8−
𝟏
𝟐
x2.(-x)
= (-x).(ln 8)8−
𝟏
𝟐
x2
Jawaban :
1. f(x) = 20log4
fꞌ(x) = 20.
𝒅
𝒅𝒙
(log4x)
= 20.
𝟏
(𝐥𝐧 𝟒)𝒙
=
𝟐𝟎
𝒙 𝐥𝐧 𝟒
2. y = log10 3x
yꞌ =
𝟏
(𝐥𝐧 𝟏𝟎) 𝟑𝒙
.
𝒅
𝒅𝒙
(3x)
=
𝟏
(𝐥𝐧 𝟏𝟎) 𝟑𝒙
(3)
=
𝟑
𝒙 𝐥𝐧 𝟏𝟎
Temukanturunan dari fungsi yang diberikan
1. f(x) = 20log4 6. f(x) = 15x2 + 10log2 x
2. y = log10 3x 7. g(x) = log6(7x-2x3)
3. g(x) = log8(5x3) 8. f(t) = log16(3t2+5t – 20)
4. y = -4log8(5x3) 9. g(t) = log2(et)
5. h(x) = log5(-10x3) 10. f(x) = log10(log10x)

9. 3. g(x) = log8(5x3)
gꞌ(x) =
𝟏
(𝐥𝐧 𝟖)𝟓𝒙 𝟑
.
𝒅
𝒅𝒙
(5x3
)
=
𝟏
(𝐥𝐧 𝟖)𝟓𝒙 𝟑
. (𝟏𝟓𝒙 𝟐
)
=
𝟑
𝒙 𝐥𝐧 𝟖
4. y = -4log8 (5x3)
yꞌ =
𝟒
(𝐥𝐧 𝟖)𝟓𝒙 𝟑
.
𝒅
𝒅𝒙
(5x3
)
=
𝟒
(𝐥𝐧 𝟖)𝟓𝒙 𝟑
.(15x2
)
=
−𝟔𝟎 𝒙 𝟐
(𝐥𝐧 𝟖)𝟓𝒙 𝟑
=
−𝟏𝟐
𝒙 𝐥𝐧 𝟖
5. h(x) = log5(-10x3)
hꞌ(x) =
𝟏
(𝐥𝐧 𝟓)−𝟏𝟎𝒙 𝟑.
𝒅
𝒅𝒙
(-10x3)
=
𝟏
(𝐥𝐧 𝟓)−𝟏𝟎𝒙 𝟑.(-30x2)
=
𝟑
𝒙 𝐥𝐧 𝟓
6. f(x) = 15x2 + 10log2 x
fꞌ(x) = 15x2 + 10.
𝒅
𝒅𝒙
.(log2 x)
= 30x + 10.
𝟏
(𝐥𝐧 𝟐)𝒙
= 30x +
𝟏𝟎
𝒙 𝒍𝒏𝟐
7. g(x) = log6(7x-2x3)
gꞌ(x) =
𝟏
(𝐥𝐧 𝟔)𝟕𝒙−𝟐𝒙 𝟑.
𝒅
𝒅𝒙
(7x-2x)
=
𝟕−𝟔𝒙 𝟐
(𝐥𝐧 𝟔)𝟕𝒙−𝟐𝒙 𝟑
=
𝟕−𝟔𝒙 𝟐
𝟕𝒙−𝟐𝒙 𝟑(𝐥𝐧 𝟔)

10. 8. f(t) = log16(3t2+5t – 20)
fꞌ(t) =
𝒅
𝒅𝒙
(log16(3t2+5t-20)
=
𝟏
(𝐥𝐧 𝟏𝟔)𝟑𝐭𝟐+𝟓𝐭−𝟐𝟎
.
𝒅
𝒅𝒙
(3t2+5t-20)
=
𝟏
(𝐥𝐧 𝟏𝟔)𝟑𝐭𝟐+𝟓𝐭−𝟐𝟎
.(6t + 5)
=
𝟔𝒕+𝟓
𝟑𝐭𝟐+𝟓𝐭−𝟐𝟎(𝐥𝐧 𝟔)
9. g(t) = log2(et)
gꞌ(t) =
𝒅
𝒅𝒙
.( log2(et))
=
𝟏
(𝐥𝐧 𝟐) 𝒆 𝒕.
𝒅
𝒅𝒙
(et)
=
𝟏
(𝐥𝐧 𝟐) 𝒆 𝒕. (et)
=
𝟏
(𝐥𝐧 𝟐)
10. f(x) = log10(log10x)
fꞌ(x) =
𝒅
𝒅𝒙
(log10(log10x))
=
𝟏
(𝐥𝐧 𝟏𝟎).(𝐥𝐨𝐠 𝟏𝟎 𝒙)
.
𝒅
𝒅𝒙
(log10 x)
=
𝟏
(𝐥𝐧 𝟏𝟎).(𝐥𝐨𝐠 𝟏𝟎 𝒙)
.
𝟏
(𝐥𝐧 𝟏𝟎).(𝐥𝐨𝐠 𝟏𝟎 𝒙)
.
𝒅
𝒅𝒙
(x)
=
𝟏
(𝐥𝐧 𝟏𝟎) 𝟐.(𝐥𝐨𝐠 𝟐 𝟏𝟎 𝒙)
Temukan turunan dari fungsi yang diberikan
1. f(x) = 5 sin 3x 6. s(t) = 4 cot5t
2. y =
𝟏
𝟒
cos(2x2) 7. g(x) = 6tan3(
𝟐𝒙
𝟑
)-20√ 𝒙
3. g(x) = 5tan(
𝟑𝒙
𝟓
) 8. f(x) = 2xsinx+cos2x
4. f(x) = 10sec2x 9. h(x) =
𝒔𝒊𝒏𝟑𝒙
𝟏+𝒔𝒊𝒏𝟑𝒙
5. y =
𝟐
𝟑
sec(2x3) 10. f(x) = e4xsin2x

11. Jawaban :
1. f(x) = 5sin3x
fꞌ(x) = 5 cos3x
𝒅
𝒅𝒙
(3x)
= 15 cos 3x
2. f(x) =
𝟏
𝟒
cos(2x2)
fꞌ(x) =
𝟏
𝟒
-sin 2x2 𝒅
𝒅𝒙
(2x2)
=
𝟏
𝟒
-sin 2x2.4x
= −
𝟒𝒙
𝟒
sin2x2
= -xsin2x2
3. g(x) = 5tan(
𝟑𝒙
𝟓
)
gꞌ(x) = 5 sec2(
𝟑𝒙
𝟓
)
𝒅
𝒅𝒙
(
𝟑𝒙
𝟓
)
= 5 sec2(
𝟑𝒙
𝟓
).
𝟑
𝟓
= 3 sec2(
𝟑𝒙
𝟓
)
4. f(x) = 10 sec 2x
fꞌ(x) = 10 sec 2x tan 2x
𝒅
𝒅𝒙
(2x)
= 20 sec 2x tan 2x
5. y =
𝟐
𝟑
sec(2x3)
yꞌ =
𝟐
𝟑
sec 2x3 tan 2x3 𝒅
𝒅𝒙
(2x3)
=
𝟐
𝟑
sec 2x3 tan 2x3.6x2
= 4x2sec 2x3 tan 2x3
6. s(t) = 4 cot 5t
sꞌ(t) = -4 csc2 5t
𝒅
𝒅𝒕
(5t)
= -20 csc2 5t

12. 7. g(x) = 6tan3(
𝟐𝒙
𝟑
)-20√ 𝒙
gꞌ(x) = 6 sec6(
𝟐𝒙
𝟑
)
𝒅
𝒅𝒙
(
𝟐𝒙
𝟑
)-10𝒙
−𝟏
𝟐⁄
= 6 sec6(
𝟐𝒙
𝟑
).(
𝟐𝒙
𝟑
) − 𝟏𝟎𝒙
−𝟏
𝟐⁄
= 4 sec6(
𝟐𝒙
𝟑
)-
𝟏𝟎
√ 𝒙
8. f(x) = 2x sinx + cos 2x
fꞌ(x) = 2 cos x
𝒅
𝒅𝒙
(x) + (-sin 2x)
𝒅
𝒅𝒙
(2x)
= 2 cos x – 2 sin 2x
9. h(x) =
𝒔𝒊𝒏𝟑𝒙
𝟏+𝒔𝒊𝒏𝟑𝒙
hꞌ(x) =
𝒄𝒐𝒔 𝟑𝒙
𝒅
𝒅𝒙
(𝟑𝒙)
𝒄𝒐𝒔 𝟑𝒙
𝒅
𝒅𝒙
(𝟑𝒙)
=
𝟑 𝒄𝒐𝒔 𝟑𝒙
𝟑 𝒄𝒐𝒔 𝟑𝒙
= 1
10. f(x) = e4xsin2x
fꞌ(x) = e4x 𝒅
𝒅𝒙
(4x). cos 2x
𝒅
𝒅𝒙
(2x)
= 4e4x.2cos 2x
Temukan turunan dari fungsi yang diberikan
1. f(x) = sin-1( -x3) 6. f(x) = cos-1(x2)
2. h(x) = cos -1(ex) 7. h(x) = csc-1(2x)
3. g(x) = tan-1(x2) 8. g(x) = 4 sec-1(
𝒙
𝟐
)
4. f(x) = cot-1(7x-5) 9. f(x) = x sin-1(7x2)
5. y =
𝟏
𝟓
sin-1(5x3) 10. y = arcsin(√𝟏 − 𝒙 𝟐)

13. Jawaban :
1. f(x) = 𝑺𝒊𝒏−𝟏
(−𝒙 𝟑
)
fꞌ(x) =
−𝟏
√ 𝟏−(−𝒙 𝟑 ) 𝟐
.
𝒅
𝒅𝒙
.(−𝒙 𝟑
)
=
−𝟑𝒙 𝟐
√ 𝟏−𝒙 𝟗
2. h(x) = cos -1(ex)
hꞌ(x) =
−𝟏
√ 𝟏−(𝒆 𝒙) 𝟐
.
𝒅
𝒅𝒙
(ex)
=
−𝒆 𝒙
√ 𝟏−(𝒆 𝒙) 𝟐
3. g(x) = tan-1(x2)
gꞌ(x) =
𝟏
𝟏+ (𝒙 𝟐) 𝟐.
𝒅
𝒅𝒙
(x2)
=
𝟐𝒙
𝟏+ 𝒙 𝟒
4. f(x) = cot-1(7x-5)
fꞌ(x) =
−𝟏
𝟏+(𝟕𝑿−𝟓) 𝟐.
𝒅
𝒅𝒙
(7x-5)
=
−𝟕
𝟒𝟗𝑿 𝟐− 𝟕𝟎𝑿+𝟐𝟓
5. y =
𝟏
𝟓
sin-1(5x3)
yꞌ =
𝟏
√ 𝟏+ (𝟓𝒙 𝟑 ) 𝟐
.
𝒅
𝒅𝒙
(5𝒙 𝟑
).
𝟏
𝟏𝟓
=
𝟏
√ 𝟏+𝟐𝟓𝒙 𝟔
.15x2.
𝟏
𝟏𝟓
=
𝟏𝟓𝒙 𝟐
√ 𝟏+𝟐𝟓𝒙 𝟔.𝟏𝟓
6. f(x) = cos-1(x2)
fꞌ(x) =
𝟏
√ 𝟏− (𝒙 𝟐 ) 𝟐
.
𝒅
𝒅𝒙
(x2)
=
−𝟐𝒙
√ 𝟏+𝒙 𝟒

14. 7. h(x) = csc-1(2x)
hꞌ(x) =
−𝟏
| 𝟐𝒙|√(𝟐𝒙) 𝟐− 𝟏
.
𝒅
𝒅𝒙
. (2x)
= -
𝟐
𝟐𝒙 √ 𝟒𝒙 𝟐 − 𝟏
8. g(x) = 4 sec-1(
𝒙
𝟐
)
gꞌ(x) = 4.
−𝟏
|
𝒙
𝟐
|√(
𝒙
𝟐
)
𝟐
.
𝒅
𝒅𝒙
.(
𝒙
𝟐
)
=
−𝟒
𝒙
𝟐
√ 𝒙 𝟐
𝟒
− 𝟏
.
𝟏
𝟒
=
−𝟒
𝒙
𝟐
√ 𝒙 𝟐
𝟒
– 𝟏 .𝟒
9. f(x) = x sin-1(7x2)
fꞌ(x) = 1.
𝟏
√ 𝟏− (𝟕𝒙 𝟐 ) 𝟐
.
𝒅
𝒅𝒙
.7x2
=
𝟏𝟒𝒙
√ 𝟏−𝟒𝟗𝒙 𝟒
10. y = arcsin(√𝟏 − 𝒙 𝟐)
yꞌ =
𝟏
√ 𝟏− (√ 𝟏− 𝒙 𝟐 )
𝟐
.
𝒅
𝒅𝒙
.√𝟏 − 𝒙 𝟐
=
𝟏
√𝟏− ( 𝟏−𝒙 𝟐 )
. 𝟏
𝟐⁄ (1 – x2)
=
𝟏−𝒙 𝟐
𝟐√ 𝒙 𝟐
Temukan turunan dari fungsi yang diberikan
1. f(x) = x7 + 2x10 , Temukan fꞌꞌꞌ(x) 6. s(t) = 16t2-
𝟐𝒕
𝟑
+10 , Temukan sꞌꞌ(t)
2. h(x) = √ 𝒙𝟑
, Temukan hꞌꞌ(x) 7. g(x) = ln3x , Temukan 𝑫 𝒙
𝟑[ 𝒈(𝒙)]
3. g(x) = 2x , Temukan g(5)(x) 8. f(t) =
𝟏𝟎
𝒙 𝟓 +
𝒙 𝟑
𝟓
, Temukan f(4)(x)
4. f(x) = 5ex , Temukan f(4)(x) 9. f(x) = 32x , Temukan fꞌꞌꞌ(x)
5. y(x) = sin3x , Temukan
𝒅 𝟑
𝒚
𝒅 𝟑 𝒙
10. y = 𝒍𝒐𝒈 𝟐5x , Temukan
𝒅 𝟒
𝒚
𝒅 𝟒 𝒙

15. Jawaban
1. f(x) = x7 + 2x10
fꞌ(x) = 7x6 + 20x9
fꞌꞌ(x) = 42x5 + 180x8
fꞌꞌꞌ(x) = 210x4 + 1440x7
2. h(x) = √ 𝒙𝟑
= 𝒙
𝟏
𝟑⁄
hꞌ(x) = 𝟏
𝟑⁄ 𝒙
𝟐
𝟑⁄
hꞌꞌ(x) =
−𝟐
𝟗
𝒙
−𝟓
𝟑⁄
3. g(x) = 2x
gꞌ(x) = 2
gꞌꞌ(x) = 0
gꞌꞌꞌ(x) = 0
g4(x) = 0
4. f(x) = 5ex
fꞌ(x) = 5ex.1
fꞌꞌ(x) = 5ex.1 = 5ex
fꞌꞌꞌ(x) = 5ex.1
=
𝒅 𝟑
𝒈
𝒅 𝟑 𝒙
= 5ex
5. y = sin 3x
𝒅 𝟏
𝒚
𝒅 𝟏 𝒙
= 3 cos 3x
𝒅 𝟐
𝒚
𝒅 𝟐 𝒙
= -9 sin 3x
𝒅 𝟑
𝒚
𝒅 𝟑 𝒙
= - 27 cos 3x
6. s(t) = 16t2 -
𝟐𝒕
𝟑
+ 10
sꞌ(t) = 32t -
𝟐
𝟑
sꞌꞌ(t) = 32

16. 7. g(x) = ln 3x
D1(x)[ 𝒈(𝒙)] =
𝟑
𝟑𝒙
=
𝟏
𝒙
= 𝒙−𝟏
D2(x)[ 𝒈(𝒙)] = −𝒙−𝟐
D3(x)[ 𝒈(𝒙)] = 𝟐𝒙−𝟑
8. f(x) =
𝟏𝟎
𝒙 𝟓 +
𝒙 𝟑
𝟓
= 𝟏𝟎𝒙−𝟓
+
𝟏
𝟓
𝒙 𝟑
fꞌ(x) = -50 𝒙−𝟔
+
𝟑
𝟓
𝒙 𝟐
fꞌꞌ(x) = 300 x-7 +
𝟔
𝟓
x
fꞌꞌꞌ(x) = -2100 x-8 +
𝟔
𝟓
f4(x) = 16800 x-9
9. f(x) = 32x
fꞌ(x) = 32x ln 3 . 2
fꞌꞌ(x) = 32x ln 3 .
𝟐
𝟑
fꞌꞌꞌ(x) = 32x ln 3 . 2 .
𝟏
𝟑
= 32x ln 3 .
𝟐
𝟗
10. g = log2 5x
𝒅ꞌ𝒚
𝒅ꞌ𝒙
=
𝟏
𝟓𝒙 𝐥𝐧 𝟐
. 5 =
𝟓
𝟓𝒙 𝐥𝐧 𝟐
𝒅ꞌꞌ𝒚
𝒅ꞌꞌ𝒙
=
𝟓
𝟓
.
𝟏
𝟐
.1
𝒅ꞌꞌꞌ𝒚
𝒅ꞌꞌꞌ𝒙
= 0 =
𝒅 𝟒
𝒚
𝒅 𝟒 𝒙
= 0