Page 23 - TUTORIAL MATEMATIKA IPA SEMESTER 2

TURUNAN FUNGSI ALJABAR

′
12. ( ) =
3 2 4
3
2
4
4
2
5(((2 + 3 ) − (5 + 3) ) ) . 2((2 + 3 ) − (5 + 3) ).
2
3
2
(4(2 + 3 ) . (4 + 3) − 3(5 + 3) . 5)

1 1
1 2 1 1 − 2 1 1
−
′
13. ( ) = (2 + (2 )2) → ( ) = (2 + (2 )2) . (2 + (2 ) 2. 2)
2 2
1
1 − 2 1
1
−
′
( ) = (2 + (2 )2) . (2 + (2 ) 2)
2

2
2 7
14. ( ) = (2 − 7 ) . (4 + 3)3
∴ ( ) = ( ). ( )
2 7
′
2 6
∴ ( ) = (2 − 7 ) → ( ) = 7(2 − 7 ) . (2 − 14 )
2 2 1 8 1
−
−
′
∴ ( ) = (4 + 3)3 → ( ) = (4 + 3) 3. (4 + 0) = (4 + 3) 3
3 3
2 8 1
−
′
2 6
2 7
( ) = 7(2 − 7 ) . (2 − 14 ). (4 + 3)3 + (2 − 7 ) . (4 + 3) 3
3
1 8
−
2
′
2 6
( ) = (2 − 7 ) . (4 + 3) 8. (7(2 − 14 )(4 + 3) + (2 − 7 ))
3

7
8
7
′
15. ( ) = 256 − 1 → ( ) = 8.256 − 0 = 2048

( −5) 3
16. ( ) =
2 2
′
3
2
∴ ( ) = ( − 5) → ( ) = 5( − 5)
′
2
∴ ( ) = 2 → ( ) = 4
3
2
2
2
2
′
( ) = 5( −5) .2 −( −5) .4 = 2 ( −5) (5 −2( −5)) = 2 ( −5) (3 +10)
2 2
(2 ) 4 4 4 2

1
(3 −1) 4 2
17. = ( + 5) →
(2− ) 3
1 3 3 4 2
−
4
1 (3 −1)
′
= ( + 5) 2 . ( 4(3 −1) .3.(2− ) −(3 −1) .3.(2− ) .−1 + 0)
3 2
2 (2− ) 3 ((2− ) )
3
2
2
3
′
= 3(3 −1) (2− ) (4(2− )+(3 −1)) = 3(3 −1) (2− ) (7− )
(2− ) 6 (2− ) 6

2
(3− ) .(3 +1) 3
18. = 1 →
2
(4 )3
1 − 2
3 1
2
2
2
3
2
(2(3− ).−1.(3 +1) + (3− ) .3(3 +1) ).(4 ) −(3− ) .(3 +1) . (4 ) 3
2 3
′
= 3
1 2
2
((4 )3)
1 − 2
1
3
2
2
2
2
3
2 3
(−2(3− )(3 +1) + 3(3− ) (3 +1) )(4 ) − (3− ) (3 +1) (4 ) 3
′
= 3
1 2
2
((4 )3)
2
−
1
2
2
2
(4 ) 3 (3− )(3 +1) ((4 (3(3− )−2(3 +1)))− (3− )(3 +1))
3
′
= 2
2
(4 )3
‘LEARNING IS FUN’ 22