Page 35 - EbooK MATEMATIKA PEMINATAN KELAS XII Yovy shelviani

B. SIFAT-SIFAT TURUNAN
f (x) = u(x).v(x) → f ' (x) = u' (x).v(x) + u(x).v' (x)

u(x) u'(x).v(x) − u(x).v'(x)
f (x) = → f '(x) =
2
v(x) v(x)

Kegiatan 4.2

Penggunaan Sifat-sifat Turunan dalam menyelesaikan persamaan Trigonometri

Tentukan turunan sebagai berikut ini (menggunakan sifat2):
2
2
1. f(x) = x .sin x → f(x)’ = (x cos x + 2x sin x)
cos x −1
2. f (x) = → f '(x) =
1+ cos x 1 + sin 2x
x
2
3
3. f (x) = → f '(x) =cos x.sin x + x sin x = sin x(cos x.sin x + x )
2 cot x

Penyelesaian

2
1) f(x) = x .sin x → f (x) = u(x).v(x)
u(x) =→ u' (x) = .......................

v(x) =→ v' (x) = .......................
f ' (x) = u' (x).v(x) + u(x).v' (x)

f ' (x) = (.................)(.................) + (................)( ..................)
f ' (x) = ........................................... = ..........................................
f ' (x) = ...........................................

cos x
2) f (x) =
sin x + cos x

u(x) = ....................... → u' (x) = .......................
v(x) = ....................... → v' (x) = .......................

u'(x).v(x) − u(x).v'(x) (.......)(............) − (.......)( ...... )
f '(x) = =
v(x) 2 ( ................ )
............................................... ...............................................
= = =
2
(.........) ....................
...............................................
= = .........
............................

x
3) f (x) =
2 cot x
u(x) = ....................... → u' (x) = .......................

33 | Matematika Peminatan SMA/MA Kelas XII