مقالات

7.1: أ- جدول المشتقات


الصيغ العامة

1. ( quad dfrac {d} {dx} left (c right) = 0 )

2. ( quad dfrac {d} {dx} left (f (x) + g (x) right) = f ′ (x) + g ′ (x) )

3. ( quad dfrac {d} {dx} left (f (x) g (x) right) = f ′ (x) g (x) + f (x) g ′ (x) )

4. ( quad dfrac {d} {dx} left (x ^ n right) = nx ^ {n − 1} ، رباعي نص {للأرقام الحقيقية} n )

5. ( quad dfrac {d} {dx} left (cf (x) right) = cf ′ (x) )

6. ( quad dfrac {d} {dx} left (f (x) −g (x) right) = f ′ (x) −g ′ (x) )

7. ( quad dfrac {d} {dx} left ( dfrac {f (x)} {g (x)} right) = dfrac {g (x) f ′ (x) −f ( س) ز ′ (س)} {(ز (س)) ^ 2} )

8. ( quad dfrac {d} {dx} left [f (g (x)) right] = f ′ (g (x)) · g ′ (x) )

الدوال المثلثية

9. ( quad dfrac {d} {dx} left ( sin x right) = cos x )

10. ( quad dfrac {d} {dx} left ( tan x right) = sec ^ 2x )

11. ( quad dfrac {d} {dx} left ( sec x right) = sec x tan x )

12. ( quad dfrac {d} {dx} left ( cos x right) = - sin x )

13. ( quad dfrac {d} {dx} left ( cot x right) = - csc ^ 2x )

14. ( quad dfrac {d} {dx} left ( csc x right) = - csc x cot x )

الدوال المثلثية المعكوسة

15. ( quad dfrac {d} {dx} left ( sin ^ {- 1} x right) = dfrac {1} { sqrt {1 − x ^ 2}} )

16. ( quad dfrac {d} {dx} left ( tan ^ {- 1} x right) = dfrac {1} {1 + x ^ 2} )

17. ( quad dfrac {d} {dx} left ( sec ^ {- 1} x right) = dfrac {1} {| x | sqrt {x ^ 2−1}} )

18. ( quad dfrac {d} {dx} left ( cos ^ {- 1} x right) = dfrac {-1} { sqrt {1 − x ^ 2}} )

19. ( quad dfrac {d} {dx} left ( cot ^ {- 1} x right) = dfrac {-1} {1 + x ^ 2} )

20. ( quad dfrac {d} {dx} left ( csc ^ {- 1} x right) = dfrac {-1} {| x | sqrt {x ^ 2−1}} )

الدوال الأسية واللوغاريتمية

21. ( quad dfrac {d} {dx} left (e ^ x right) = e ^ x )

22. ( quad dfrac {d} {dx} left ( ln | x | right) = dfrac {1} {x} )

23. ( quad dfrac {d} {dx} left (b ^ x right) = b ^ x ln b )

24. ( quad dfrac {d} {dx} left ( log_bx right) = dfrac {1} {x ln b} )

وظائف الزائدية

25. ( quad dfrac {d} {dx} left ( sinh x right) = cosh x )

26. ( quad dfrac {d} {dx} left ( tanh x right) = text {sech} ^ 2 ، x )

27. ( quad dfrac {d} {dx} left ( text {sech} x right) = - text {sech} ، x tanh x )

28. ( quad dfrac {d} {dx} left ( cosh x right) = sinh x )

29. ( quad dfrac {d} {dx} left ( coth x right) = - text {csch} ^ 2 ، x )

30. ( quad dfrac {d} {dx} left ( text {csch} ، x right) = - text {csch} x coth x )

الدوال القطعية المعكوسة

31. ( quad dfrac {d} {dx} left ( sinh ^ {- 1} x right) = dfrac {1} { sqrt {x ^ 2 + 1}} )

32. ( quad dfrac {d} {dx} left ( tanh ^ {- 1} x right) = dfrac {1} {1-x ^ 2} quad (| x | <1) )

33. ( quad dfrac {d} {dx} left ( text {sech} ^ {- 1} ، x right) = dfrac {-1} {x sqrt {1-x ^ 2 }} رباعي (0

34. ( quad dfrac {d} {dx} left ( cosh ^ {- 1} x right) = dfrac {1} { sqrt {x ^ 2-1}} quad (x> 1) )

35. ( quad dfrac {d} {dx} left ( coth ^ {- 1} x right) = dfrac {1} {1-x ^ 2} quad (| x |> 1) )

36. ( quad dfrac {d} {dx} left ( text {csch} ^ {- 1} ، x right) = dfrac {-1} {| x | sqrt {1 + x ^ 2}} رباعي (س ≠ 0) )


شاهد الفيديو: What is the Monte Carlo method? Monte Carlo Simulation in Finance. Pricing Options (شهر نوفمبر 2021).