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Kalkulus

Kalkulus. Aturan-aturan Diferensial. leibniz's notation. d y. f '( x ). D x f ( x ). d x. theorem A. D x ( k ). = 0. theorem B. D x ( x ). = 1. theorem C. D x ( x n ). = n x n- 1. theorem C. D x ( x - n ). = - n x - n- 1. theorem D. D x [ k . f ( x )]. = k . D x [ f ( x )].

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Kalkulus

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  1. Kalkulus Aturan-aturan Diferensial Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  2. leibniz'snotation dy f'(x) Dxf(x) dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  3. theoremA Dx(k) = 0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  4. theoremB Dx(x) = 1 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  5. theoremC Dx(xn) = nxn-1 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  6. theoremC Dx(x-n) = -nx-n-1 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  7. theoremD Dx[k.f(x)] = k.Dx[f(x)] Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  8. theoremE Dx[f(x) + g(x)] = Dxf(x) + Dxg(x) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  9. theoremF Dx[f(x) - g(x)] = Dxf(x) - Dxg(x) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  10. theoremG Dx[f(x)g(x)] = Dxf(x) . Dxg(x) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  11. theoremG Dx[f(x)g(x)] = f(x)Dxg(x)+g(x)Dxf(x) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  12. f(x) = (x2 + 2)(x3 + 1) ? f'(x) = Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  13. theoremH Dx[f(x) / g(x)] g(x)Dxf(x) – f(x)Dxg(x) g2(x) = Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  14. 3 1 – f(x) = x3 x4 ? f'(x) = Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  15. Kalkulus Diferensial Trigonometri Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  16. Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  17. sin x < x < tan x Untuk tiap 0 < x < π/2 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  18. tan x < x < sin x Untuk tiap -π/2 < x < 0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  19. sin x < x < tan x sin x sin x sin x Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  20. 1 < x < 1 sin x cos x Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  21. lim = 1 1 x0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  22. 1 lim = 1 cos x x0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  23. x lim = 1 sin x x0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  24. sin x lim = 1 x x0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  25. 1-cos x lim = 0 x x0 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  26. theoremA Dx(sin x) = cos x Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  27. theoremB Dx(cos x) = -sin x Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  28. nexttheorem Dx(tan x) = sec2x Dx(sec x) = secx tanx = -cosec2x Dx(cotan x) Dx(cosec x) = -cosec x cotan x Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  29. GottfriedLeibniz “ Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof ” Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

  30. GottfriedLeibniz Monad Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

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