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TURUNAN By. Noviana Pratiwi, M.Sc.
RUMUS-RUMUS TURUNAN
1. 2. Untuk u dan v suatu fungsi,c bilangan Real
dan n bilangan Rasional berlaku y = u v y = v u y = c.u y = c.u y = u.v y = u v + u.v
naxy 1 nnaxy
2' ''
vuvvuy
vuy o
f(x) = 3x2 + 4 f1(x) = 6x
f(x) = 2(x)3 + 12x2 8x + 4
f1(x) = 6x2 + 24x 8
f(x) = (3x-2)(4x+1)
f(x) = 12x2 + 3x 8x 2
f(x) = 12x2 5x 2
f1(x) = 24x 5
1-6 2x x32 f(x)
1-1-1-61 (-1).x 2 x326. (x)f
22x - 4x (x)f -51
3 x y 6 3 xy 2
6
3 xy 3 21 3x y
f(x) = (2x 1)3
f1(x) = 3(2x 1)2 (2)
f1(x) = 6(2x 1)2
f1(x) = 6(2x 1)(2x 1)
f1(x) = 6(4x2 4x+1)
f1(x) = 24x2 24x + 6
f(x) = (5x2 1)2
f1(x) = 2(5x2 1) (10x)
f1(x) = 20x (5x2 1)
f1(x) = 100x3 20x
3x4x f(x) 2
21
3x) (4x f(x) 2
3)(8x 21
3x)2(4x21 (x)f1
21
3x)2)(4x23(4x (x)f1
f(x) = (3x2 6x) (x + 2)
Cara 1:
Misal : U = 3x2 6x U1 = 6x 6
V = x + 2 V1 = 1
Sehingga:
f1(x) = (6x 6)(x+2)+(3x2+6x).1
f1(x) = 6x2+12x 6x 12+3x2 6x
f1(x) = 9x2 12
4 V 1 -4x V
3 U 23x U
:Misal1-4x23x f(x)
1
1
21
2
111
1)(4x
2)4(3x1)3(4x(x)f
V
UV -VU(x)f
:Maka
TUGAS !!!!!!
Hal.: 18
TURUNAN / DEFERENSIAL Rumus rumus turunan fungsi trigonometri
TURUNAN
Contoh 1
xxy sin2 Carilah turunan fungsi trigonometri
Jawab
Misalkan Maka,
xuxu 2'2 o xvxv cos'sin o
''' uvvuy ))(cos())(sin2( 2 xxxx
xxxx cossin2 2
TUGAS !!!!!!
Penggunaan Turuan
TUGAS !!!!!!
TUGAS !!!!!!
TUGAS !!!!!!
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