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TURUNAN FUNGSI ALJABAR

TURUNAN FUNGSI ALJABAR. LAMBANG TURUNAN. y = f(x). KONSEP LIMIT. Contoh : Tentukanlah turunan pertama dari x n Jawab. = = =. RUMUS TURUNAN FUNGSI ALJABAR. f(x) = x n  f ’ (x) = nx n-1. Contoh : Tentukanlah turunan pertama dari x 7 Jawab Dik . n = 7 Dit f ’ ( x)

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TURUNAN FUNGSI ALJABAR

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  1. TURUNAN FUNGSI ALJABAR

  2. LAMBANG TURUNAN y = f(x)

  3. KONSEP LIMIT

  4. Contoh : Tentukanlahturunanpertamadarixn Jawab

  5. = = =

  6. RUMUS TURUNAN FUNGSI ALJABAR f(x) = xn  f ’(x) = nxn-1

  7. Contoh : Tentukanlahturunanpertamadari x7 Jawab Dik. n = 7 Dit f ’(x) f ’(x) = nxn-1 = 7x6

  8. SIFAT-SIFAT TURUNAN FUNGSI ALJABAR

  9. 1 f(x) = k f ’x) = 0 ; k = konstanta Contoh : Tentukanturunanpertamadari f(x) = k Jawab : f ’ (x) = 0

  10. 2 f(x) = axn f ’ (x) = anxn-1 ; a R Contoh : Tentukanturunankeduadari f(x) = 10x-4

  11. Jawab : Dik. a = 10 n = -4 Dit. f 2(x)  f ’ (x) = a.nxn-1 f ”(x) = a.n.(n-1)xn-2 f ” (x) = 10.-4.(-4-1)x-4-2 f ” (x) = 10.-4.(-5)x-6 = 200x-6

  12. 3 f(x) = u(x) ± v(x) f ’(x) = u’(x) ± v’(x) Contoh : Tentukanturunanpertamadari f(x) = 2x3 + 5x-2 - 8

  13. Jawab : Dik. u(x) = 2x3 v(x) = 5x-2 w(x) = -8 Dit. f ’(x)  f ’(x) = u’(x) ± v’(x) ± w’(x) = 6x2 -10x-3 – 0 = 6x2 -10x-3

  14. 4 f(x) = k.u(x)n f1(x) = k. n.u’(x).u(x) ; k,n = konstanta Contoh : f(x) = 5(4x + 3)2

  15. Jawab : Dik k = 5 n = 2 u(x) = (4x+3) Ditf1(x) f1(x) = k. n.u’ (x).u(x) = 5.2.4.(4x + 3) = 40(4x + 3) = 160x + 120

  16. 5 f(x) = u(x).v(x)  f1(x) = u’(x).v(x) + u(x).v’(x) Contoh :   f(x) = 2(x3 +5x2)

  17. Jawab : Dik u(x) = 2 v(x) = (x3 +5x2) Ditf1(x) f1(x) = u’(x).v(x) + u(x).v’(x) = 0. (x3 +5x2) + 2(3x2 +10x) = 6x2 +20x

  18. 6  Contoh :

  19. Jawab : Dik u(x) = x2 v(x) = (4x + 1) Dit f ’(x)

  20. LATIHAN SOAL UN

  21. LATIHAN 1 Turunan pertama dari x2 + 2 – 1/x adalah A. 2x + x2D. B. C.E. x3 + 2x – x-2

  22. JAWAB  X2 + 2 – X-1 • f(x) = u(x) ± v(x) f1(x) = u’(x) ± v’(x) = 2x + 0 – (-1.x-2) = 2x + x-2  D

  23. LATIHAN 1 Diketahui A. D. B. E. C.

  24. JAWAB  A

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