Page 24 - Kelas XII_Matematika Peminatan_KD 3.3

2. f(x) = 3x – cos x untuk x = 1
3 1
f'(x) = 3 – (-sin x) 1
1
f'(x) = 3 + sin x 1

f'( ) = 3 + sin ( )
3 3
1

f'( ) = 3 + √3
3 2

3. ( ) =
5 + 1
Misalkan:
= → ′ = −
= 5 + → ′ = 1

′ − ′ 1
′ ( ) = 1
2 1
(− )(5 + ) −
′ ( ) =
(5 + ) 2

2
2
−5 − −
′ ( ) =
(5 + ) 2
2
2
−5 − ( + )
′ ( ) =
(5 + ) 2
−5 − 1
′ ( ) =
(5 + ) 2
4 a. = 3 + cos
Untuk 3x.sin x dimisalkan: 1
= 3 → = 3 1
′
= sin → = cos 1
′
′ 1
4b. = 3. sin + 3 . cos + (− sin )
′
= 3 sin − sin + 3 . cos 1
′
= 2 sin + 3

3
= 2 −
Untuk 2x.cos x dimisalkan: 1
′
= 2 → = 2 1
′
= cos → = − sin 1
′
2
= 2. (cos ) + 2 . (− sin ) − 3 1
2
′
= 2 cos − 2 − 3 1

Skor Maksimum 30

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