Reglas

1. Constante:ddx

c = 0 2. Múltiplo constante:ddx

cf (x) = c f (x)

. Suma:ddx

[ f (x) ± g(x)] = f (x) ± g (x) 4. Producto:ddx

f (x)g(x) = f (x)g (x) + g(x) f (x)

5. Cociente:ddx

f (x)g(x)

= g(x)f (x) f (x)g (x)

[g(x)]26. Cadena:

ddx

f (g(x)) = f (g(x))g (x)

7. Potencia:ddx

xn = nxn 1 8. Potencia:ddx

[g(x)]n = n[g(x)]n 1 g (x)

Funciones

Trigonométricas:

9.ddx

senx = cos x 10.ddx

cos x = senx 11.ddx

tan x = sec2 x

12.ddx

cot x = csc2 x 13.ddx

sec x = sec x tan x 14.ddx

csc x = csc x cot x

Trigonométricas inversas:

15.ddx

sen 1 x = 1

1 x216.

ddx

cos 1 x = 1

1 x217.

ddx

tan 1 x = 1

1 + x2

18.ddx

cot 1 x = 1

1 + x219.

ddx

sec 1 x = 1

x x2 120.

ddx

csc 1 x = 1

x x2 1

Hiperbólicas:

21.ddx

senhx = cosh x 22.ddx

cosh x = senhx 23.ddx

tanh x = sech2 x

24.ddx

coth x = csch2 x 25.ddx

sech x = sech x tanh x 26.ddx

csch x = csch x coth x

Hiperbólicas inversas:

27.ddx

senh 1 x = 1

x2 + 128.

ddx

cosh 1 x = 1

x2 129.

ddx

tanh 1 x = 1

1 x2

30.ddx

coth 1 x = 1

1 x231.

ddx

sech 1 x = 1

x 1 x232.

ddx

csch 1 x = 1

x x2 + 1

Exponencial:

33.ddx

ex = ex 34.ddx

bx = bx (ln b)

Logarítmica:

35.ddx

ln x = 1x

36.ddx

logb x = 1x(ln b)

3

LISTA DE DERIVADAS

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BREVE TABLA DE INTEGRALES

1.1

, 11

nn uu du C n

n2.

1 lndu u Cu

3. u ue du e C 4.1

lnu ua du a C

a

5. sen cosu du u C 6. cos senu du u C

7. 2sec tanu du u C 8. 2csc cotu du u C

9. sec tan secu u du u C 10. csc cot cscu u du u C

11. tan ln cosu du u C 12. cot ln senu du u C

13. sec ln sec tanu du u u C 14. csc ln csc cotu du u u C

15. sen sen cosu u du u u u C 16. cos cos senu u du u u u C

17. 2 1 12 4sen sen 2u du u u C 18. 2 1 1

2 4cos sen 2u du u u C

19. 2tan tanu du u u C 20. 2cot cotu du u u C

21. 23 13sen 2 sen cosu du u u C 22. 23 1

3cos 2 cos senu du u u C

23. 3 212tan tan ln cosu du u u C 24. 3 21

2cot cot ln senu du u u C

25. 3 1 12 2sec sec tan ln sec tanu du u u u u C 26. 3 1 1

2 2csc csc cot ln csc cotu du u u u u C

27.sen( ) sen( )sen cos

2( ) 2( )a b u a b u Cudubuaa b a b

28.sen( ) sen( )cos cos

2( ) 2( )a b u a b u Cudubuaa b a b

29. 2 2sen sen cosau

au ee bu du a bu b bu Ca b

30. 2 2cos cos senau

au ee bu du a bu b bu Ca b

31. senh coshu du u C 32. cosh senhu du u C

33. 2sech tanhu du u C 34. 2csch cothu du u C

35. tanh ln(cosh )u du u C 36. coth ln senhu du u C

37. ln lnu du u u u C 38. 2 21 12 4ln lnu u du u u u C

39. 1

2 2

1 sen udu Caa u

40. 2 2

2 2

1 lndu u a u Ca u

41.2

2 2 2 2 1sen2 2u a ua u du a u C

a42.

2222222 ln

2 2u aa u du a u u a u C

43. 12 2

1 1 tan udu Ca aa u

44. 2 2

1 1 ln2

a udu Ca a ua u

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