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Modul Matematika Peminatan Kelas XII KD 3.3

− ′
′
( ) =
′
2
(− sin )(1 + cos ) − (cos )(− sin )
′
( ) =
(1 + cos )
2
− sin − sin cos + cos sin
′
( ) =
(1 + cos )
2
− sin
′
( ) =
(1 + cos )
2
cos
c. ( ) =
sin +cos
pilih u = cos x  u = –sin x
v = sin x + cos x  v
= cos x –sin x
cos
( ) = =
sin + cos
maka
−
′
′
( ) =
′
2
(− sin )(sin + cos ) − (cos )(cos − sin )
′
( ) =
(sin + cos )
2

−sin − sin cos − cos + cos sin
2
2
( ) = 2 2
′
sin + cos + 2 sin cos
−(sin + cos )
2
2
( ) = (2 sin cos = sin 2 )
′
1 + sin 2
−1
( ) = (cos + sin = 1)
′
2
2
1 + sin 2

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