turunan/diferensial sma kelas xii
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TURUNAN/TURUNAN/ DIFERENSIAL DIFERENSIAL
TURUNAN/TURUNAN/ DIFERENSIAL DIFERENSIAL
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DEFINISI TURUNAN
h
f(x)-h)f(x lim
0h (x)f y
dx
dy
:dengan kandidefinisi
xterhadap f(x) ydari Turunan
11
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RUMUS-RUMUS TURUNAN
1.
2. Untuk u dan v suatu fungsi,c bilangan Real dan n bilangan Rasional berlaku– y = u ± v → y’ = v’ ± u’– y = c.u → y’ = c.u’– y = u.v → y’ = u’ v + u.v’
naxy 1 nnaxy
2' ''
v
uvvuy
v
uy
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Soal ke-1
Jika f(x) = 3x2 + 4 maka nilai f1(x)
yang mungkin adalah ….
A. 3x C. 9x2 E. 12x2
B. 6x D. 10x2
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Pembahasan
f(x) = 3x2 +
4
f1(x) = 6xwww.meetabied.wordpress.co
m
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Jawaban soal ke-1
Jika f(x) = 3x2 + 4 maka nilai f1(x)
yang mungkin adalah ….
A. 3x C. 9x2 E. 12x2
B. 6x D. 10x2
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Soal ke-2
Nilai turunan pertama dari:
f(x) = 2(x)2 + 12x2 – 8x + 4 adalah …
A. x2 – 8x + 5 D. 6x2 + 24x + 8
B. 2x2 – 24x – 2 E. 6x2 + 24x – 8
C. 2x2 + 24x – 1 www.meetabied.wordpress.co
m
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Pembahasan
f(x) = 2x3 + 12x3 – 8x
+ 4
f1(x) = 6x2 + 24x – 8
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Jawaban soal ke-2
Nilai turunan pertama dari:
f(x) = 2(x)2 + 12x2 – 8x + 4 adalah …
A. x2 – 8x + 5 D. 6x2 + 24x + 8
B. 2x2 – 24x – 2 E. 6x2 + 24x – 8
C. 2x2 + 24x – 1 www.meetabied.wordpress.co
m
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Soal ke-3
Turunan ke- 1 dari f(x) = (3x-2)(4x+1)
Adalah …
A. 24x + 5 D. 12x – 5
B. 24x – 5 E. 12x – 10
C. 12x + 5 www.meetabied.wordpress.co
m
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Pembahasan
f(x) = (3x-2)(4x+1)
f1(x) = 12x2 + 3x – 8x –
2
f(x) = 12x2 – 5x – 2
f1(x) = 24x – 5www.meetabied.wordpress.co
m
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Jawaban soal ke-3
Turunan ke- 1 dari f(x) = (3x-2)(4x+1)
Adalah …
A. 24x + 5 D. 12x – 5
B. 24x – 5 E. 12x – 10
C. 12x + 5 www.meetabied.wordpress.co
m
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Soal ke- 4
1-5
2-51-5
1-55
1-61
2x 4x C.
2x 4x E. 2x 2x B.
2x 4x D. 2x 2x A.
adalah... 2x x32 f(x) dari (x)f Nilai
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Pembahasan
22x - 4x (x)f
(-1).x 2 x326. (x)f
2x x32 f(x)
-51
1-1-1-61
1-6
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Jawaban Soal ke- 4
1-5
2-51-5
1-55
1-61
2x 4x C.
2x 4x E. 2x 2x B.
2x 4x D. 2x 2x A.
adalah... 2x x32 f(x) dari (x)f Nilai
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Soal ke- 5
3 3x D. 3x B.
1 x3 E. 2 x3 C. x3 A.
... adalah 3 x y dari 1-ke Turunan
22
6
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Pembahasan
21
3
26
6
3x y
3 xy
3 xy
3 x y
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Jawaban Soal ke- 5
3 3x D. 3x B.
1 x3 E. 2 x3 C. x3 A.
... adalah 3 x y dari 1-ke Turunan
22
6
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Soal ke- 6
Jika f(x) = (2x – 1)3 maka nilai f1(x)
adalah …
A. 12x2 – 3x + 12 D. 24x2 – 12x + 6
B. 12x2 – 6x – 3 E. 24x2 – 24x + 6
C. 12x2 – 6x + 3
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Pembahasanf(x) = (2x – 1)3
f1(x) = 3(2x – 1)2 (2)
f1(x) = 6(2x – 1)2
f1(x) = 6(2x – 1)(2x – 1)
f1(x) = 6(4x2 – 4x+1)
f1(x) = 24x2 – 24x + 6
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Jawaban Soal ke- 6
Jika f(x) = (2x – 1)3 maka nilai f1(x) adalah
…
A. 12x2 – 3x + 12 D. 24x2 – 12x + 6
B. 12x2 – 6x – 3 E. 24x2 – 24x + 6
C. 12x2 – 6x + 3
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Soal ke- 7
Turunan pertama dari f(x) = (5x2 – 1)2
adalah …
A. 20x3 – 20x D. 5x4 – 10x2 + 1
B. 100x3 – 10x E. 25x4 – 10x2 + 1
C. 100x3 – 20x
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Pembahasan
f(x) = (5x2 – 1)3
f1(x) = 2(5x2 – 1) (10x)
f1(x) = 20x (5x2 – 1)
f1(x) = 100x3 – 20x
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Jawaban Soal ke- 7
Turunan pertama dari f(x) = (5x2 – 1)2
adalah …
A. 20x3 – 20x D. 5x4 – 10x2 + 1
B. 100x3 – 10x E. 25x4 – 10x2 + 1
C. 100x3 – 20x
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Soal ke- 8
32
21-
2
22
2
3x) - (4x )23 -(4x C.
3x) - (4x )23 (4x E. 3) (2x 4x)-
32( B.
3x) (4x )23 -(4x D. 8) (2x 4)-x
32( A.
adalah... 3x 4x f(x) dari pertama Turunan
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Pembahasan
21
3x)2)(4x23(4x (x)f
3)(8x 21
3x)2(4x21 (x)f
21
3x) (4x f(x)
3x4x f(x)
1
1
2
2
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Jawaban Soal ke- 8
32
21
-2
22
2
3x) - (4x )23 -(4x C.
3x) - (4x )23 (4x E. 3) (2x 4x)-
32
( B.
3x) (4x )23 -(4x D. 8) (2x 4)-x
32
( A.
adalah... 3x 4x f(x) dari pertama Turunan
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Soal ke- 9
Turunan pertama dari
f(x) = (3x2 – 6x) (x + 2)
adalah …
A. 3x2 – 12 D. 9x2 – 12
B. 6x2 – 12 E. 9x2 + 12
C. 6x2 + 12 www.meetabied.wordpress.co
m
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Pembahasan
f(x) = (3x2 – 6x) (x + 2)
Cara 1:
Misal : U = 3x2 – 6x
U1 = 6x – 6
V = x + 2
V1 = 1www.meetabied.wordpress.com
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Pembahasan
Sehingga:
f1(x) = (6x – 6)
(x+2)+(3x2+6x).1
f1(x) =6x2+12x – 6x – 12+3x2 –
6x
f1(x) =9x2 – 12www.meetabied.wordpress.com
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Pembahasan
f(x) = (3x2 – 6x) (x + 2)
Cara 2:
f1(x) = 3x-3+6x2 – 6x3 –
12x
f1(x) = 9x2+12x –12x – 12
f1(x) = 9x2 – 12www.meetabied.wordpress.co
m
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Jawaban Soal ke- 9
Turunan pertama dari
f(x) = (3x2 – 6x) (x + 2)
adalah …
A. 3x2 – 12 D. 9x2 – 12
B. 6x2 – 12 E. 9x2 + 12
C. 6x2 + 12 www.meetabied.wordpress.co
m
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Soal ke- 10
1-8x-24x C.
18x-16x
11- E. 18x16x B.
1-8x-24x D. 18x-16x A.
... adalah 1-4x2)(3x
f(x) dari pertama Turunan
2
22
22
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Pembahasan
4 V
1 -4x V 3 U
23x U :Misal
1-4x23x f(x)
1
1
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Pembahasan
21
2
111
1)(4x
2)4(3x1)3(4x(x)f
V
UV -VU(x)f
:Maka
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Pembahasan
18x16x
11(x)f
18x16x
812x312x(x)f
21
21
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Jawaban Soal ke- 10
1-8x-24x C.
18x-16x
11- E. 18x16x B.
1-8x-24x D. 18x-16x A.
... adalah 1-4x2)(3x
f(x) dari pertama Turunan
2
22
22
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Soal ke- 11
32 D.
34
B.
31 E. 1 C.
35 A.
... adalah mungkin yangNilai 4. (x)1f Jika
6 4x -23xf(x) Diketahui
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Pembahasan
f(x) = 3x2 – 4x + 6
f1(x) = 6x – 4
Jika f1(x) = 4
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Pembahasan
34x
68x
86x6x86x44
46x4:Maka
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Jawaban Soal ke- 11
32 D.
34
B.
31 E. 1 C.
35 A.
... adalah mungkin yangNilai 4. (x)1f Jika
6 4x -23xf(x) Diketahui
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Soal ke- 12
Diketahui f(x) = 5x2+3x+7. Nilai f1(-2)
Adalah ….
A. -29 D. -7
B. -27 E. 7
C. -17
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Pembahasan
f(x) = 5x2 – 3x + 7
f1(x) = 10x – 3
Maka untuk f1(-2)
adalah…
f1(-2) = 10(-2)+3
f1(-2) = -20+3
f1(-2) = -17www.meetabied.wordpress.com
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Jawaban Soal ke- 12
Diketahui f(x) = 5x2+3x+7. Nilai f1(-2)
Adalah ….
A. -29 D. -7
B. -27 E. 7
C. -17
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Soal ke- 13
3 D. 3 - B.
6 E. 0 C. 6 - A.
... adalah 211f Nilai
16 5x 24x -32xf(x) Diketahui
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Pembahasan
... adalah 21
f untuk Maka
12-12x(x)f
512x-6x(x)f
16-5x6x-2xf(x)
"
"
2"
23
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Pembahasan
6- 21
f
12- 6 21
f
12 - 21
12 21
f
"
"
"
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Jawaban Soal ke- 13
3 D. 3 - B.
6 E. 0 C. 6 - A.
... adalah 211f Nilai
16 5x 24x -32xf(x) Diketahui
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Soal ke- 14
34x)-2(2x 12)-(18x (x)1f E.
34x)-2(3x 12)-(18x (x)1f D.
34x)-2(3x 12)-(18x (x)1f C.
52)2(3x 2)-(18x (x)1f B.
51)-2(3x 12)-(18x (x)1f A.
62 adalah... 4x3x21 f(x) dari pertama Turunan
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Pembahasan
52
52
162
62
4x)12)(3x(18x(x)1f
4)(6x4x)3(3x(x)1f
4)(6x4x)(3x21
6.(x)1f
4x)(3x21
f(x)
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Jawaban Soal ke- 14
54x)-212)(2x-(18x (x)1f E.
54x)-212)(3x-(18x (x)1f D.
54x)-212)(3x-(18x (x)1f C.
52)22)(3x-(18x (x)1f B.
51)-212)(3x-(18x (x)1f A.
62 adalah... 4x3x21 f(x) dari pertama Turunan
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Soal ke- 15
34
D.32
B.
35
E.1 C.31
A.
12
adalah... mungkin x yangnilai maka
)21
(f untuk 1 3x 6x f(x) Diketahui
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Pembahasan
x2
3-12x 21
:maka21
(x)f untuk
3-12x (x)f
13x 26xf(x)
1
1
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Pembahasan
31 x
248
x
8 24x
24x 8
24x 62
624x 2
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Jawaban Soal ke- 15
34
D.32
B.
35
E.1 C.31
A.
12
adalah... mungkin x yangnilai maka
)21
(f untuk 1 3x 6x f(x) Diketahui
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Soal ke- 16
4-8x D.28x B.
48x E. 2-8x C.1x A.
adalah... 1-2x f(x)
:dari pertama Turunan
4
4
8
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Pembahasan
2
48
1)-(2xf(x)
1)-(2xf(x)
1)-(2xf(x) 4 8
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Pembahasan
48x(x)f
1)4(2x(x)f
1)(2)2(2x(x)f
1
1
1
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Jawaban Soal ke- 16
4-8x D.28x B.
48x E. 2-8x C.1x A.
adalah... 1-2x f(x)
:dari pertama Turunan
4
4
8
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Soal ke- 17
1 D. 1 - B.
2531
E. 0 C.2531
- A.
adalah...
mungkin x yangnilai Maka 2. yuntuk
1-2x y dari pertama Turunan1
3
6
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Pembahasan
6)-10(5xy
(5) 6)-2(5xy
6)-(5xy
6)-(5xy
6)(5x y
1
36
3 6
2
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Pembahasan
2531
x
5062
x
6250x
50x602
60-50x2
:maka 2, yUntuk 1
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Jawaban Soal ke- 17
1 D. 1 - B.
2531
E. 0 C.2531
- A.
adalah...
mungkin x yangnilai Maka 2. yuntuk
1-2x y dari pertama Turunan1
3
6
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