Page 10 - Kelas XII_Matematika Peminatan_KD 3.3

( ) = sin

( + ℎ) = sin( + ℎ)

Maka = ( ) = lim ( +ℎ)− ( ) = lim ( +ℎ)−sin
ℎ→0 ℎ ℎ→0 ℎ
2 ( +ℎ+ ) ( +ℎ− )
= lim 2 2
ℎ→0 ℎ Ingat !
2 +ℎ ℎ ( + ) ( − )
2 ( ) ( ) Sin A – sin B = 2cos sin
= lim 2 2
ℎ→0 ℎ
1
cos ( 2 + ℎ) ℎ
= lim( 2 2 )
ℎ→0 1 ℎ
2
1
1 sin ℎ
2
= lim cos( + ℎ)
ℎ → 0 2 1 ℎ
2
1
1 sin ℎ
2
= lim cos( + ℎ) ℎ→0
ℎ → 0 2 1 ℎ
2
1
= cos (x + 0).1
2
= cos x

y’ = f’(x) = cos x

2. Sekarang coba tentukan turunan dari y = f(x) = cos x.

Alternatif penyelesaian:
Ingat !
( ) = cos cos A – cos B = -2sin
( + ) ( − )
( + ℎ) = cos( + ℎ) sin

Maka = ( ) = lim ( +ℎ)− ( ) = lim ( +ℎ)−co
ℎ→0 ℎ ℎ→0 ℎ
−2 ( +ℎ+ ) ( +ℎ− )
= lim 2 2
ℎ→0 ℎ
ℎ
−2 ( 2 +ℎ ) ( )
= lim 2 2
ℎ→0 ℎ
2 +ℎ) 1
−2sin ( ℎ
= lim( 1 2 2 )
ℎ→0 ℎ
2
1
1 sin ℎ
2
= lim −sin( + ℎ)
ℎ → 0 2 1 ℎ
2
= ….

Apakah hasilnya sama?

y’=f’(x) = -sin x

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