Page 24 - TUTORIAL_MAT_IPA_K11-2

TURUNAN FUNGSI ALJABAR

−
19. ( ) =
−
−
→ (1) = = 1 → − = 1 − → 2 − 1 = … ( )
1−
′
→ ( ) = = 2 → = 2
1
Dari (i) → = 2.2 − 1 = 3
2.2−3
→ (2) = = −1
1−2

20. ( ) = ( o )( )
∴ ingat aturan rantai
′
′
′
′( ) = ( ( ( ))) . ( ). ( )
′
′
′
′
′
′
′
(0) = ( ( (0))). (0). (0) = ( (0)). (0). 2 = (0). 2.2 = 2.2.2 = 8

21. ℎ( ) = ( ( ))
∴ ingat aturan rantai
′
′
′
′
′
′
′
ℎ ( ) = ( ( )). ( ), ℎ (4) = ( (4)). (4) = (4). 2 = 4.2 = 8

3
′
2
′
22. ( ) = 0.(2 ( )−1) −1.3(2 ( )−1) .(2 ( )−0) ,
(2 ( )−1) 3
2
2
′
(0) = 0−3(2 (0)−1) .2 ′(0) = −3(2.1−1) .2.2 = −12
(2 (0)−1) 3 (2.1−1) 3

′
′
′
23. ∴ ( . ) (2) = (2) (2) + (2) (2) = 11 → 3 (2) + 4 (2) = 11 … ( )
′
2 ′
2
′
∴ ( + ) (2) = 2 (2) (2) + 2 (2) (2) = 2 (2). 3 + 2 (2). 4 = 20
→ 3 (2) + 4 (2) = 10 … ( )
Eliminasi (i) dan (ii) → (2) = 2 , (2) = 1
′ ′
(2) (2)− (2) ′(2) 3.1−2.4
( ) (2) = = = −5
( (2)) 2 1 2

2
24. ∴ ( ). ( ) = − 3
′
′
→ ( ) ( ) + ( ) ( ) = 2 − 3
′
′
→ (1) (1) + (1) (1) = 2.1 − 3 = −1
′
′
∴ (1) = (1) = (1), (1) = 2
′
2
′
′
′
′
→ 2 (1) + (1) (1) = −1 → { (1)} + 2 (1) + 1 = 0
′
′
′
2
→ { (1) + 1} = 0 → (1) + 1 = 0 → (1) = −1

2
25. ( ) = ( + 2)
∴ ingat aturan rantai
′
2
′( ) = ( + 2). 2
2
′
′
→ (1) = (1 + 2). 2.1
′
→ 2 = (3). 2
′
→ (3) = 1

‘LEARNING IS FUN’ 23