Page 22 - E-Modul ajar matematika

Contoh Soal:

Dengan menggunakan konsep turunan, tentukan turunan pertama dari :

1. ( ) =10
Jawab:

Karena f (x) = 10 merupakan fungsi konstanta ( tetap) maka f ( x + ∆x ) = 10 (tetap)

( + ∆ ) − ( ) 10 − 10 0
′
( ) = lim = lim = lim = lim 0 = 0
∆ →0 ∆ ∆ →0 ∆ ∆ →0 ∆ ∆ →0

2. ( ) =3 +5
Jawab:

( ) = 5 + 3 f(x + Δx) = 3 (x + Δx) + 5 = 3x + 3Δx + 5
′
2
( + ∆ ) − ( ) 3( + ∆ ) + 5 − (3 + 5)
′
( ) = lim = lim
∆ →0 ∆ ∆ →0 ∆

3 + 3∆ + 5 − 3 − 5 3∆
= lim = lim = lim 3 = 3
∆ →0 ∆ ∆ →0 ∆ ∆ →0

3. ( ) = 5 2+3

Jawab:

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

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