Page 25 - TUTORIAL MATEMATIKA IPA SEMESTER 2

TURUNAN FUNGSI ALJABAR

26.
6 u(x)

4 v(x)

3 6

′
( ) = ( ). ( ) , (5) = ⋯
Pertama-tama tentukan dahulu persamaan garis u(x) dan v(x).
∴ ingat rumus menentukan persamaan garis jika titik potong dengan sumbu X dan sumbu Y
Diketahui : + =
∴ ( )
′
→ 6 + 6 ( ) = 36 → + ( ) = 6 → ( ) = 6 − → ( ) = −1
∴ ( )
4
( ) = , 0 ≤ < 3
( ) = { 3
4, ≥ 3
′
Karena yang diminta pada x = 5 maka ( ) = 4 → ( ) = 0
′
′
′
∴ ( ) = ( ) ( ) + ( ) ( )
′
′
′
→ (5) = (5) (5) + (5) (5) = −1.4 + 1.0 = −4

27. ∴ ingat aturan rantai dan aturan perkalian
′
′
(3 + 2). 3 = 1. √ + 1 + → 3 (3 + 2) = 1. √ + 1 +
2√ +1 2√ +1
∴ 11 = 3 + 2 → 9 = 3 → = 3
3
′
′
′
3 (11) = √3 + 1 + 3 → 3 (11) = √4 + 3 = 2 + = 11 → (11) = 11
2√3+1 2√4 4 4 12
′
→ 12 (11) = 12. 11 = 11
12

2
28. ( ) ( ) = ( + 2),

′ ′ ′
( ) ( )− ( ) ( ) ′ 2
→ ( ) ( ) = 2 = ( + 2). 2
( ( ))
′
(1) (1)− (1) ′(1)
′
2
→ = (1 + 2). 2.1
( (1)) 2
2.3−(−2).−1 4 2
′
′
′
→ = 2 (3) → 2 (3) = → (3) =
(3) 2 9 9

2
′
29. ( ) = + 4 + 1 → ( ) = 2 + 4
′
2
∴ ( ) = √10 −
′
′
′
2
2
( ) ( ) = ( ( )). ( ) = √10 − ( + 4 + 1) . (2 + 4)
′
2
2
( ) (0) = √10 − (0 + 4.0 + 1) . (2.0 + 4) = √9. 4 = 12

‘LEARNING IS FUN’ 24