Formulario derivadas e integrales

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Derivadas
u,v,w = expresiones algebraicas; a,b,c,n = constantes
1.

d
dx

c=0

2.

d
dx

x =1

3.

d
dx

=
( u + v + w)

4.

d
dx

( c ⋅ v ) =c ⋅

5.

d
dx

6.d

11. dx

(u ⋅ v) =

d
dx

d
dx

u⋅

d
dx

u+

d
dx

v+

d
dx

w

v
v + v⋅

d
dx

u

d
( v ) = n ( v ) dx v
d
dx ( x )= n ⋅ x

14.

v

d

v −1

=
(sen v )

8.

9.

d
dx

d
dx

d

10. dx

 u
 v
 u
 c

v⋅ u −u⋅
d
dx

=

=

v

2

u

c
d
dx

( ln v ) =

=
( tan v )

d
sec v ⋅ dx v
2

d
dx

(sec v ) = sec v ⋅ tan v ⋅

d
− csc
( csc v ) = v ⋅ cot v ⋅ dx v

v
21. dx ( arcsen v ) =
d

2

d
dx

v

d
dx

v=

d

27. dx

2

v

v −1
2



d
dx

v

v v −12

d
v ⋅ dx v

d
dx

v

1+ v

( arccsc v ) =

d

26. dx

− csc
( cot v ) =

20. dx

v

v

2

d
dx

d

v

d

18. dx

2

v

1+ v

24. dx ( arccot v ) = −− sen d
( cos v ) = v ⋅ dx v

17. dx

19.

d
dx

d
dx

25. dx ( arcsec v ) =

d

v
d
dx

d
dx

v

1− v

d

d

16. dx

n −1

n

v

d
cos v ⋅ dx v

d

7.( arctan v ) =
dx
d

23.

u

v

d

d
dx

22. dx ( arccos v ) = −

v

u

u

15. dx

n −1

n

u

12. dx
13.

d
dx

d
( a ) =a ⋅ ln a ⋅ dx u
d
d
)
dx ( e = e ⋅dx u
d
d
v
⋅ dx u + ln u ⋅ u
dx ( u ) =⋅ u
d

d
dx

log e

( log v ) =

v

2 v

d
dx v

1− v

2

ELABORÓ: PROF. JESÚS CALIXTO SUÁREZ
Integrales inmediatas
1.

∫ ( du + dv+ dw) = ∫ du + ∫ dv + ∫ dw

11.

∫ csc

2.

∫ a dv = a ∫ dv

12.

v dv
∫ sec v tan =

3.

∫ dx=

13.

− csc
∫ csc v cot v dv = v + C

14.

∫ tan v d

15.



x+C

dv∫v=

v

n

4.


5.

dv

n +1

v dv = v + C
− cot


21.

sec v + C

6.
v

a

23.

cot v dv ln sen v + C
=
ln ( sec v + tan v ) + C

17.

ln a

∫ csc v dv=...
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