TURUNAN MATEMATIKA.pdf

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 !!!!!!