Page 15 - E-Modul

Contoh Soal:

Dengan menggunakan konsep turunan, tentukan turunan pertama dari:
1. ( ) = 10

Jawaban:

Karena ( ) = 10 merupakan gungsi konstan (tetap) maka ( + ∆ ) =
10 ( )
( + ∆ ) − ( ) 10 − 10 0
′
( ) = lim = lim = lim = lim 0 = 0
∆ →0 ∆ ∆ →0 ∆ ∆ →0 ∆ ∆ →0

2. ( ) = 3 + 5

Jawaban:
( ) = 3 + 5 ( + ∆ ) = 3( + ∆ ) + 5 = 3 + 3∆ + 5

( + ∆ ) − ( ) 3( + ∆ ) + 5 − (3 + 5)
′
( ) = lim = lim
∆ →0 ∆ ∆ →0 ∆
3 + 3∆ + 5 − 3 − 5 3∆
= lim = lim = lim 3 = 3
∆ →0 ∆ ∆ →0 ∆ ∆ →0

3. ( ) = 5 + 3
2
Jawaban:
2
2
2
( + ∆ ) = 5( + ∆ ) + 3 = 5( + 2 . ∆ + ∆ ) + 3
2
2
= 5 + 10 . ∆ + 5∆ + 3
( + ∆ ) − ( )
′
( ) = lim
∆ →0 ∆
2
2
2
5 + 10 . ∆ + 5∆ + 3 − (5 + 3)
= lim
∆ →0 ∆
2
2
2
5 + 10 . ∆ + 5∆ + 3 − (5 + 3)
= lim
∆ →0 ∆
10 . ∆ + 5∆ 2 10 . ∆ 5∆ 2
= lim = lim + lim
∆ →0 ∆ ∆ →0 ∆ ∆ →0 ∆
= lim 10 + lim 10 = 10 + 0 = 10
∆ →0 ∆ →0

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