tugas matematika kelompok
TRANSCRIPT
TUGAS MATEMATIKA KELOMPOK
“ DIFRENTIATION : HALAMAN 33-40 “
Disusun Oleh :
Nama : 1.Achmad Trybuana Kurniasandy
2.Aulia Ramadhani
3.Barry Alkhafi
4.Faizal
Kelas : 1 EA
Semester : 2 ( DUA )
POLITEKNIK MANUFAKTUR NEGERI BANGKA BELITUNG
2014/2015Kawasan Industri Air Kantung, Sungailiat-Bangka 33211
Telp : 0717-93586, 95252 Faks : 0717-93585E-mail : [email protected]
Website : http://polman-babel.ac.id
Temukan turunan dari fungsi yang diberikan1. f(x) = 20ex 6. f(x) = 15x2 +10ex
2. y = e3x 7. g(x) = e7x−2x3
3. g(x) = e5x3
8. f(t) = 100
e−0.5 t
4. y = -4e5x3
9. g(t) = 2500e2t+1
5. h(x) = e−10 x3
10. f(x) = 1
√2 πex2
2
“ HALAMAN 33-40 “
Jawaban :
1. f(x) = 20ex
fꞌ(x) = 20.ddx
(ex)
= 20ex
2. y = e3x
yꞌ(x) = e3x.ddx
(5x3)
= e5x3
(15x2)
= 15x2e5x3
3. g(x) = e5x3
gꞌ(x) = e5x3
(.ddx
(5x3)
= e5x3
( (15x2)
= 15x2e5x3
4. y = -4e5x3
yꞌ= -4.ddx
(e5x3
)
= -4.e5x3
.ddx
(5x3)
= -4.e5x3
(15x2)
= -60x2e5x3
5. h(x) = e−10 x3
hꞌ(x) = e−10 x3
.ddx
(-10x3)
= e−10 x3
(-30x2)
= -30x2e−10 x3
6. f(x) = 15x2 + 10ex
fꞌ(x) = 15x2 + 10.ddx
(ex)
= 30x + 10ex
7. g(x) = e7x−2x3
gꞌ(x) = e7x−2x3
.ddx
(7x-2x3)
= e7x−2x3
(7-6x)
= 7-6xe7x−2x3
8. f(t) = 100e−0.5 t
fꞌ(t) = 100.e0.5t
= 100. e0.5t.ddx
(0.5t)
= 100. e0.5t(0.5)
= 50e0.5t
9. g(t) = 2500e2t+1
gꞌ(t) = 2500e2t+1.ddx
(2t+1)
= 2500e2t+1.(2)
= 5000e2t+1
10. f(x) = 1
√2 π ex22
fꞌ(x) = 1
√2 π .e12
x2.ddx
(12
x2)
= 1
√2 π .e12
x2.(x)
= x
√2 π .e12
x2
Jawaban :
1. f(x) = 20 ln x
fꞌ(x) = 20 . ddx
(ln x)
= 20.1x
= 20x
2. y = ln 3x
yꞌ = 13x
. ddx
(3x)
= 13x
. (3x)
= 1x
3. g(x) = ln(5x3)
gꞌ(x) = 1
5x3 . ddx
(5x3)
= 1
5x3.(15x2)
= 3x
4. y = - 4 ln (5x3)
yꞌ = - 4.1
5x3.ddx
(5x3)
Temukan turunan dari fungsi yang diberikan1. 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)
= - 4. 1
5x3.(15x2)
= -4.3x
= - 12x
5. h(x) = ln(-10x3)
hꞌ(x) = 1
−10x3 . ddx
(-10x3)
= 1
−10x3(-30x2)
= 3x
6. f(x) = 15x2 + 10ln x
fꞌ(x) = 15x2 + 10.ddx
(ln x)
= 30x + 10.1x
= 30x + 10x
7. g(x) = ln(7x-2x3)
gꞌ(x) = 1
7 x−2x3.ddx
(7x-2x3)
= 1
7 x−2x3. (7x-2x3)
= 7−6 x2
7 x−2x3
8. f(t) = ln(3t2 + 5t – 20)
fꞌ(t) = 1
3t 2+5 t−20.ddx
(3 t 2+5 t−20¿
= 1
3t 2+5 t−20. (6 t+5 )
= 6 t+5
3t 2+5 t−20
9. g(t) = ln(et)
gꞌ(t) = 1
et . ddx
(et)
=1
et(e)
= e
et
10. f(x) = ln(ln x)
fꞌ(x) = 1ln x
. ddx
(ln x)
= 1ln x
. (1x
)
= 1
ln x . x
Jawaban :
1. f(x) = 20 (3x)
fꞌ(x) = 20.ddx
(3x)
= 20(ln3)3x
2. y = 53x
yꞌ = (ln 5)53x.ddx
(3x)
Temukan turunan dari fungsi yang diberikan
1. f(x) = 20 (3x) 6. f(x) = 15x2 + 10(5x3)
2. y = 53x 7. g(x) = 37 x−2 x3
3. g(x) =25 x3
8. f(t) = 100
10−0.5 t
4. y = -4(25 x3
) 9. g(t) = 2500(52t+1)
5. h(x) = 4−10 x3
10. f(x) = 8 x2
2
= (ln 5)53x.(3)
= 3(ln 5)53x
3. g(x) = 25 x3
gꞌ(x) = (ln 2)25 x3
.ddx
(5x3)
= (ln 2)25 x3
(15x2)
= 15x2(ln 2)25 x3
4. y = -4(25 x3
)
yꞌ = -4.ddx
(25 x3
)
= -4(ln 2)25 x3
.(15x2)
= -60x2(ln 2)25 x3
5. h(x) = 4−10 x3
hꞌ(x) = (ln 4)4−10 x3.ddx
(-30x2)
= (ln 4)4−10 x3. (-30x2)
= -30x2(ln 4)4−10 x3
6. f(x) = 15x2 + 10(5x3)
fꞌ(x) = 15x2 + 10.ddx
(53x)
= 30x + 10(ln 5)53.3
= 30x + 30(ln 5)53
7. g(x) = 37 x−2 x3
gꞌ(x) = (ln 3)37 x−2 x3
.ddx
(7x-2x3)
= (ln 3)37 x−2 x3
.(7-6x2)
= 7-6x2(ln 3)37 x−2 x3
8. f(t) = 100
10−0.5 t
fꞌ(t) = 100. 100.5t
= 100.(ln 10)100.5t.ddx
(0.5t)
= 100.(ln 10)100.5t. 0.5 = 50(ln 10)100.5t
9. g(t) = 2500(52t+1)
gꞌ(t) = 2500.ddx
(52t+1)
= 2500(ln 5)52t+1.ddx
(2t+1)
= 2500(ln 5)52t+1.2
= 5000(ln 5)52t+1
10. f(x) = 8 x2
2
= 8−12
x2
fꞌ(x) = (ln 8)8−12
x2.ddx
(−12
x2)
= (ln 8)8−12
x2.(-x)
= (-x).(ln 8)8−12
x2
Temukan turunan 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)
Jawaban :
1. f(x) = 20log4
fꞌ(x) = 20.ddx
(log4x)
= 20. 1¿¿
= 20x ln 4
2. y = log10 3x
yꞌ = 1¿¿
.ddx
(3x)
= 1¿¿ (3)
= 3
x ln 10
3. g(x) = log8(5x3)
gꞌ(x) = 1¿¿
.ddx
(5x3)
= 1¿¿
= 3x ln 8
4. y = -4log8 (5x3)
yꞌ = 4¿¿
.ddx
(5x3)
= 4¿¿ .(15x2)
= −60 x2
¿¿
= −12x ln 8
5. h(x) = log5(-10x3)
hꞌ(x) = 1¿¿
.ddx
(-10x3)
= 1¿¿
.(-30x2)
= 3x ln 5
6. f(x) = 15x2 + 10log2 x
fꞌ(x) = 15x2 + 10.ddx
.(log2 x)
= 30x + 10. 1¿¿
= 30x + 10x ln 2
7. g(x) = log6(7x-2x3)
gꞌ(x) = 1¿¿
.ddx
(7x-2x)
= 7−6 x2
¿¿
= 7−6 x2
7 x−2x3 ¿¿
8. f(t) = log16(3t2+5t – 20)
fꞌ(t) = ddx
(log16(3t2+5t-20)
= 1¿¿
.ddx
(3t2+5t-20)
= 1¿¿ .(6t + 5)
= 6 t+5
3t 2+5 t−20¿¿¿
9. g(t) = log2(et)
gꞌ(t) = ddx
.( log2(et))
= 1¿¿
.ddx
(et)
= 1¿¿ . (et)
= 1¿¿
10. f(x) = log10(log10x)
fꞌ(x) = ddx
(log10(log10x))
= 1¿¿
.ddx
(log10 x)
= 1¿¿
. 1¿¿
.ddx
(x)
= 1¿¿
Temukan turunan dari fungsi yang diberikan
1. f(x) = 5 sin 3x 6. s(t) = 4 cot5t
2. y = 14
cos(2x2) 7. g(x) = 6tan3( 2x3 )-20√ x
3. g(x) = 5tan( 3 x5 ) 8. f(x) = 2xsinx+cos2x
4. f(x) = 10sec2x9. h(x) =
sin 3 x1+sin 3x
5. y = 23
sec(2x3)10. f(x) = e4xsin2x
Jawaban :
1. f(x) = 5sin3x
fꞌ(x) = 5 cos3xddx
(3x)
= 15 cos 3x
2. f(x) = 14
cos(2x2)
fꞌ(x) = 14
-sin 2x2 ddx
(2x2)
= 14
-sin 2x2.4x
= −4 x4
sin2x2
= -xsin2x2
3. g(x) = 5tan( 3 x5 )gꞌ(x) = 5 sec2( 3 x5 ) ddx (3 x5 ) = 5 sec2( 3 x5 ).35 = 3 sec2( 3 x5 )
4. f(x) = 10 sec 2x
fꞌ(x) = 10 sec 2x tan 2xddx
(2x)
= 20 sec 2x tan 2x
5. y = 23
sec(2x3)
yꞌ = 23
sec 2x3 tan 2x3 ddx
(2x3)
= 23
sec 2x3 tan 2x3.6x2
= 4x2sec 2x3 tan 2x3
6. s(t) = 4 cot 5t
sꞌ(t) = -4 csc2 5t ddt
(5t)
= -20 csc2 5t
7. g(x) = 6tan3( 2x3 )-20√ x
gꞌ(x) = 6 sec6( 2x3 ) ddx ( 2 x3 )-10x−12
= 6 sec6( 2x3 ).( 2x3 )−10 x−12
= 4 sec6( 2x3 ) - 10
√x
8. f(x) = 2x sinx + cos 2x
fꞌ(x) = 2 cos x ddx
(x) + (-sin 2x)ddx
(2x)
= 2 cos x – 2 sin 2x
9. h(x) = sin 3 x1+sin 3x
hꞌ(x) = cos3 x
ddx
(3x )
cos3 xddx
(3x )
= 3cos3 x3cos3 x
= 1
10. f(x) = e4xsin2x
fꞌ(x) = e4x ddx
(4x). cos 2xddx
(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( x2 )
4. f(x) = cot-1(7x-5) 9. f(x) = x sin-1(7x2)
5. y = 15
sin-1(5x3) 10. y = arcsin(√1−x2 )
Jawaban :
1. f(x) = sin−1(−x3)
fꞌ (x) = −1
√1−¿¿¿ . ddx
.¿)
= −3 x2
√1−x9
2. h(x) = cos -1(ex)
hꞌ(x) = −1
√1−(ex)2.ddx
(ex)
= −e x
√1−(ex)2
3. g(x) = tan-1(x2)
gꞌ(x) = 1
1+(x2)2.ddx
(x2)
= 2 x
1+ x4
4. f(x) = cot-1(7x-5)
fꞌ(x) = −1
1+(7 X−5)2.ddx
(7x-5)
= −7
49 X2−70 X+25
5. y = 15
sin-1(5x3)
yꞌ = 1
√1+(5 x3)2.ddx
(5x3).115
= 1
√1+25 x6 .15x2.115
= 15 x2
√1+25 x6 .15
6. f(x) = cos-1(x2)
fꞌ(x) = 1
√1−(x2)2.ddx
(x2)
=−2 x
√1+x4
7. h(x) = csc-1(2x)
hꞌ(x) = −1
|2 x|√(2x )2−1. ddx
. (2x)
= - 2
2x √4 x2−1
8. g(x) = 4 sec-1( x2 )
gꞌ(x) = 4.
−1
|x2|√( x2 )2 .ddx
.( x2 )
=
−4
x2 √ x24 −1
. 14
=
−4
x2 √ x24 – 1.4
9. f(x) = x sin-1(7x2)
fꞌ(x) = 1.1
√1−(7 x¿¿2)2¿.ddx
.7x2
= 14 x
√1−49 x4
10. y = arcsin(√1−x2 )
yꞌ = 1
√1−(√1−x2 )2.ddx
.√1−x2
= 1
√1−(1−x2 ) . 12
(1 – x2)
= 1−x2
2√ x2
Temukan turunan dari fungsi yang diberikan
1. f(x) = x7 + 2x10 , Temukan fꞌꞌꞌ(x)6. s(t) = 16t2-
2t3
+10 , Temukan sꞌꞌ(t)
2. h(x) = 3√ x , Temukan hꞌꞌ(x) 7. g(x) = ln3x , Temukan D x3 [ g(x )]
3. g(x) = 2x , Temukan g(5)(x)8. f(t) =
10
x5+ 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 d3 yd3 x
10. y = log 25x , Temukan d4 yd4 x
Jawaban
1. f(x) = x7 + 2x10
fꞌ(x) = 7x6 + 20x9
fꞌꞌ(x) = 42x5 + 180x8
fꞌꞌꞌ(x) = 210x4 + 1440x7
2. h(x) = 3√ x = x13
hꞌ(x) = 13
x23
hꞌꞌ(x) = −29x
−53
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
= d3gd3 x
= 5ex
5. y = sin 3x
d1 yd1 x
= 3 cos 3x
d2 yd2 x
= -9 sin 3x
d3 yd3 x
= - 27 cos 3x
6. s(t) = 16t2 - 2t3
+ 10
sꞌ(t) = 32t - 23
sꞌꞌ(t) = 32
7. g(x) = ln 3x
D1(x)[ g(x )] = 33x
= 1x
= x−1
D2(x)[ g(x )] = −x−2
D3(x)[ g(x )] = 2 x−3
8. f(x) = 10
x5 + x
3
5 = 10 x−5 +
15
x3
fꞌ(x) = -50 x−6 + 35
x2
fꞌꞌ(x) = 300 x-7 + 65
x
fꞌꞌꞌ(x) = -2100 x-8 + 65
f4(x) = 16800 x-9
9. f(x) = 32x
fꞌ(x) = 32x ln 3 . 2
fꞌꞌ(x) = 32x ln 3 . 23
fꞌꞌꞌ(x) = 32x ln 3 . 2 . 13
= 32x ln 3 . 29
10. g = log2 5x
d ꞌ yd ꞌ x
= 1
5x ln 2 . 5 =
55x ln 2
d ꞌꞌ yd ꞌꞌ x
= 55
. 12
.1
d ꞌꞌꞌ yd ꞌꞌꞌ x
= 0 =d4 yd4 x
= 0