TURUNAN MATEMATIKA.pdf

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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 !!!!!!