Post on 05-Dec-2015
description
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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