Page 22 - TUTORIAL MATEMATIKA IPS KELAS XI-2

TURUNAN FUNGSI ALJABAR

JAWABAN

1. lim ( + )− ( ) = lim 2( + )+3−(2 +3) = lim 2 +2 +3−2 −3 = lim 2 = 2
→0 →0 →0 →0

2
2
2
2. lim ( +ℎ)− ( ) = lim 2( + ) −2 2 = lim 2( +2 + )−2 2 =
ℎ→0 ℎ →0 →0
4 +2 2 (4 +2 )
lim = lim = 4 + 2.0 = 4
→0 →0

2
3. ( ) = 4 4−1 − 3.3 3−1 + 2.2 2−1 + 1.25 1−1 − 0 = 4 − 9 + 4 + 25
3
′

′
4
3
4. ( ) = 5.7 5−1 − 4.11 4−1 + 2.25 2−1 − 0 = 35 − 44 + 50

2
-1
-2
-4
5. ( ) = 1 + 5 − + 1 → g(x)= x + 5x - 2x +1
4 2
2
-2
'
-5
-3
g (x)=-4x -4-1 +(-2).5x -2-1 -(-1).2x -1-1 +0= -4x -10x +2x =- 4 - 10 +
x 5 x 3 x 2

1
1
1 2 2 15 15 15
1
2
√
√
6. ( ) = 3 3 √ 3 √3 = (3 (3 (3 (3 )2) ) ) = (3 )16 = 3 16. 16
15
15
1
15
′
( ) = 15 . 3 16. 16 −1 = 15 3 16. − 16
16 16

2
7. (2 − 2) = + 3 − 5
Tentukan dahulu fungsi ( ) dengan cara sebagai berikut:
+2
Misal: = (2 − 2) → =
2
2
+2 +2 1 2 5 1 2 5
→ ( ) = ( ) + 3 ( ) − 5 = + − 1 → ( ) = + − 1
2 2 4 3 4 3
1
1
5
5
′
→ ( ) = 2. 2−1 + 1−1 − 0 = +
4 3 2 3

2
8. ( ) = 7.2( − 4 + 3 − 10) 7−1 . (3 − 2.4 + 3 − 0)
3
2
′
′
2
6
2
3
( ) = 14( − 4 + 3 − 10) . (3 − 8 + 3)

4
2
2
9. ℎ ( ) = −5(42 − 11 ) 5−1 . (2.42 − 11) = −5(42 − 11 ) . (84 − 11)
′

2 −1 1 1 1 − 1 2 2 1 1 − 1
1
1
2
1
2
3
2
′
10. = ( 3 − 3) 3 . − 3 −1 = − ( 3 − 3) 3 . − 3 = − − 3 ( 3 − 3)
3 3 9 9

′
5 2
4
2
3
11. ( ) = 3(5 + (2 − 3) ) . (3.5 + 5(2 − 3) . 2)
′
2
3
5 2
4
( ) = 3(5 + (2 − 3) ) . (15 + 10(2 − 3) )

‘LEARNING IS FUN’ 21