Jawaban:

Soal turunan fungsi aljabar 15 soal dan jawaban

Pembahasan :

Materi :

(1) y = a xⁿ

=> y' = an xⁿ ⁻ ¹

(2) y = a uⁿ

=> y' = an uⁿ ⁻ ¹ . u'

(3) y = u . v

=> y' = u' v + v' u

(4) y = u/v

=> y' = (u' v - v' u)/v²

1) Jika f(x) = 2x³ - 5x² + x - 1, maka f'(x) = ....

Jawab :

f'(x) = 6x² - 10x + 1

2) Diketahui f(x) = 5x² + 4x - 3, nilai f'(2) = ....

Jawab :

f'(x) = 10x + 4

f'(2) = 10(2) + 4 = 24

3) Diketahui f(x) = 3x² - 5x + 2 dan g(x) = x² + 3x - 3. Jika h(x) = f(x) - 2g(x) maka h'(x) = ....

Jawab :

h(x) = f(x) - 2g(x)

h(x) = (3x² - 5x + 2) - 2(x² + 3x - 3)

h(x) = 3x² - 5x + 2 - 2x² - 6x + 6

h(x) = x² - 11x + 8

h'(x) = 2x - 11

4) Turunan pertama dari f(x) = 3x² + x - (1/x) + (2/x²) adalah ...

Jawab :

f(x) = 3x² + x - x⁻¹ + 2x⁻²

f'(x) = 6x + 1 + x⁻² - 4x⁻³

f'(x) = 6x + 1 + (1/x²) - (4/x³)

5) Jika f(x) = 3x² - 2ax + 7 dan f'(1) = 0 maka f'(2) = ....

Jawab :

f'(x) = 6x - 2a

f'(1) = 6(1) - 2a = 0

=> -2a = -6

=> a = 3

f'(2) = 6(2) - 2(3) = 12 - 6 = 6

6) f(x) = (3x + 2)(x - 7), f'(x) = ...

Jawab :

f(x) = 3x² - 21x + 2x - 14

f(x) = 3x² - 19x - 14

f'(x) = 6x - 19

7) Jika f(x) = 2(3x + 1)⁶, maka f'(x) = .....

Jawab :

f'(x) = 12(3x + 1)⁵ . 3

f'(x) = 36(3x + 1)⁵

8) Jika f(x) = 2(x² - 5x + 2)⁵, maka f'(x) = ....

Jawab :

f'(x) = 10(x² - 5x + 2)⁴ . (2x - 5)

f'(x) = 10(2x - 5)(x² - 5x + 2)⁴

9) Jika f(x) = 3x² (x + 1)³, maka f'(1) = ...

Jawab :

u = 3x² => u' = 6x

v = (x + 1)³ => v' = 3(x + 1)² . 1

f'(x) = u' v + v' u

f'(x) = 6x (x + 1)³ + 3(x + 1)² . 3x²

f'(1) = 6(1) (1 + 1)³ + 3(1 + 1)² . 3(1)²

f'(1) = 6 (2)³ + 3(2)² . 3

f'(1) = 48 + 36

f'(1) = 84

10) Jika f(x) = (3x - 5)/(2x + 1), maka f'(x) = ....

Jawab :

u = 3x - 5 => u' = 3

v = 2x + 1 => v' = 2

f'(x) = (u' v - v' u)/v²

f'(x) = (3(2x + 1) - 2(3x - 5))/(2x + 1)²

f'(x) = (6x + 3 - 6x + 10)/(2x + 1)²

f'(x) = 13/(2x + 1)²

11) Jika f(x) = 5/(2x - 1), maka f'(x) = ...

Jawab :

f(x) = 5(2x - 1)⁻¹

f'(x) = -5(2x - 1)⁻² . 2

f'(x) = -10/(2x - 1)²

12) Jika y = (x² + 1)(x³ - 1) maka y' = ...

Jawab :

y = x⁵ + x³ - x² - 1

y' = 5x⁴ + 3x² - 2x

13) Jika f(x) = px² + 5x - 2 dan f'(1) = 3 maka p = ...

Jawab :

f'(x) = 2px + 5

f'(1) = 2p(1) + 5 = 3

=> 2p = -2

=> p = -1

14) Jika f(x) = 8/(3x - 1)², maka f'(x) = ...

Jawab :

f(x) = 8(3x - 1)⁻²

f'(x) = -16(3x - 1)⁻³ . 3

f'(x) = -48/(3x - 1)³

15) Jika f(x) = (5x³ - 4x² + 6)/(2x), maka f'(x) = ....

Jawab :

f(x) = (5x³)/(2x) - (4x²)/(2x) + 6/(2x)

f(x) = (5/2)x² - 2x + 3x⁻¹

f'(x) = 5x - 2 - 3x⁻²

f'(x) = 5x - 2 - (3/x²)

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Kelas: 11

Mapel: Matematika

Kategori: Turunan

Kata kunci: Turunan pertama pada aljabar

Kode: 11.2.8 (Kelas 11 Matematika Bab 8 - Turunan)

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