Soal turunan fungsi al jabar 15 soal dan 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)