Document 9653528
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Transcript Document 9653528
Matakuliah
Tahun
: Kalkulus-1
: 2009
TURUNAN FUNGSI EKSPONEN, LOGARITMA,
TRIGONOMETRI & INVERS TRIGONOMETRI-2
Pertemuan-6:
Turunan Fungsi Trigonometri
Turunan Fungsi Invers Trigonometri
Turunan Fungsi Trigonometri
y sin(f ( x )) y ' cos(f ( x )).f '( x )
y cos(f ( x )) y ' sin(f ( x )).f '( x )
y tan(f ( x )) y ' sec (f ( x )).f '( x )
2
y cot(f ( x )) y ' cosec 2 (f ( x )).f '( x )
y sec(f ( x )) y ' sec(f ( x )).tan(f ( x )).f '( x )
y cosec(f ( x )) y ' cosec(f ( x )).cot( f ( x )).f '( x )
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3
Contoh-contoh:
1
y sin(2 x )
2
3
y sin ( 2 x )
y cos(2 x 1)
y tan (5 3 x )
y cosec 4 x
y cot 3x
y sec 2 x
2
4
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y cos(3 2 x )
3
3
4
Turunan Fungsi Invers Trigonometri
y arc sin f ( x ) y '
y arc cos f ( x ) y '
1
1 (f ( x ))
2
1
1 (f ( x ))
2
.f '( x )
.f '( x )
1
.f '( x )
2
1 (f ( x ))
1
y arc cot f ( x ) y '
.f '( x )
1 (f ( x ))2
1
y arc sec f ( x ) y '
.f '( x )
2
f ( x ) (f ( x )) 1
y arc tan f ( x ) y '
y arc cos f ( x ) y '
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1
f ( x ) (f ( x )) 1
2
.f '( x )
5
Contoh-contoh:
•
•
•
•
•
•
y=arc sin 2x
y=arc cos 3x
y=arc tan 4x
y=arc cot 5x
y=arc sec 6x
y=ar cosec 7x
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6
Turunan Fungsi Implisit
• Bentuk fungsi implisit: f(x,y)=0
• Contoh: Cari dy/dx dari
a. x2 + y2 = 25 di titik (4, 3)
b. 3x2 + 7y2 =10 di titik (1,1)
c. 4x3 + 6y3 – 1 = 0
d. x4 + y4 = 1
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7