Formulario De Derivadas

ACADEMIA
ACADEMIA THADER.

Tabla de derivadas
Matemáticas

1.

y=a

y′ = 0

27.

2.

y = a ⋅ xn

y ′ = n ⋅ a ⋅ x n -1

y = sec x

28.

y = ( f )n
4. y = L(x)
3.

5.

y =L(f )

6.

y = log a ( x)

7.

y = log a ( f )

y = sec( f )
29. y = cos ecx

y ′ = n ⋅ ( f ) n−1 ⋅ f ′
1
y′ =
x
f′
y′ =
f
1
y ′ = ⋅ log a (e)
x
f′
y′ = ⋅ log a (e)
f

8.y = ax
y=a

y = ex
y = ef

12.

y=n f

32.
33.

y′ = e x

11.

y = arcsenx

y′ = f ′ ⋅ e f
f′
y′ =
n ⋅ n ( f ) n −1
y′ = f ′ ⋅ g + g ′ ⋅ f
f ′ ⋅ g − g′ ⋅ f
y′ =
g2
y′ =cos x
y′ = f ′ ⋅ cos( f )

y = arcsen( f )
y = arccos x

y = arccos( f )

y′ = f ′ ⋅ a ⋅ L ( a )

10.

y = cos ec( f )

31.

y′ = a x ⋅ L ( a )

9.

30.

f

y = f ⋅g
f
14. y =g
15. y = senx
13.

16.

y = sen( f )

y = sen n ( f )
18. y = cosx
17.

19.

y = cos( f )

20.

y = cos n ( f )

21.

y = tgx

34.

f

35. y = arctgx
36.

y = arctg (f )

37. y = arc cot gx
38.

y = arc cot g ( f )

39. y = arc sec x

y′ = n ⋅ sen n −1 (f ) ⋅ f ′ ⋅ cos(f )
y′ = − senx

y′ = -f ′ ⋅ sen (f )

40.

y = arc sec( f )

y′ = − n ⋅ cos n−1 ( f ) ⋅ f ′ ⋅ sen( f

41. y = arccos ecx

1
= 1 + tg 2 x
2
cos x
f′
y′ =
= f ′ ⋅ 1 + tg 2 ( f
2
cos ( f )

42.

y′ =

22.

y = tg ( f )

23.

y = tg n ( f )

24.

y =cot gx

25.

y = cot g ( f )

y′ =

26.

y = cot g n ( f )

y ′ = − n ⋅ cot g n −1 ( f ) ⋅

[

y′ = n ⋅ tg n −1 ( f ) ⋅
y′ =

f′
cos 2 ( f )

−1
= − 1 + cot g 2 x
2
sen x

(−f ′

sen 2 (f )
f′
sen 2 ( f )

)

y = arccos ec( f )

y ′ = sec x ⋅ tgx
y′ = f ′ ⋅ sec( f ) ⋅ tg ( f )
y′ = − cos ecx ⋅ cot gx
y′ = − f ′ ⋅ cos ec( f ) ⋅ cot g ( f )

y′ =
y′ =y′ =
y′ =
y′ =
y′ =

1
1 − x2
f′
1 − (f )2

−1
1 − x2
− f′
1− ( f )

2

1
1 + x2
f′

1+ ( f )
−1
y′ =
1 + x2
− f′
y′ =
2
1+ ( f )
1
y′ =
x ⋅ x2 − 1

y′ =
y′ =...