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Cálculo Fórmulas Básicas de Derivación
LA DERIVADA
∀ u = f(x) , ∀ v = g(x) , ∀ c , e , n ∈ ℝ , a ∈ ℝ+ − {1} , e = 2.7182818284 5904523536 0287471352 …
1.
d
(c) = 0
dx
13.
d
1 d
(u)
(ln(u)) =
dx
u dx
2.
d
(x) = 1
dx
14.
d
d
cos(u) = −sen(u) (u)
dx
dx
3.
d
d
(cu) = c (u)
dx
dx
15.
d
d
tan(u) = sec2 (u) (u)
dx
dx
4.
d
d
d
(u ± v) =
(u) ±
(v)
dx
dx
dx
16.
d
d
cot(u) = −csc2 (u) (u)
dx
dx
5.
d
d
d
(uv) = u (v) + v (u)
dx
dx
dx
17.
d
d
sec(u) = sec(u)tan(u) (u)
dx
dx
d
d
v (u) − u (v)
d u
dx
dx
6.
( )=
dx v
v2
18.
d
d
csc(u) = −csc(u)cot(u) (u)
dx
dx
19.
d
1
d
(u)
arcsen(u) =
dx
√1 − u2 dx
d n
d
(u ) = nun−1 (u)
7.
dx
dx
8.
d v
d
d
(u ) = vuv−1 (u) + uv ln(u) (v)
dx
dx
dx
20.
d
−1
d
(u)
arccos(u) =
2
dx
dx
√1 − u
9.
d u
d
(a ) = au ln(a) (u)
dx
dx
21.
d
1
d
(u)
arctan(u) =
dx
1 + u2 dx
10.
d u
d
(e ) = eu
(u)
dx
dx
22.
d
−1
d
(u)
arccot(u) =
dx
1 + u2 dx
11.
d
u d
(|u|) =
(u)
|u| dx
dx
23.
d
1
d
(u)
arcsec(u) =
2
dx
dx
u √u − 1
12.
d
1
d
(u)
(loga (u)) =
dx
u ln(a) dx
24.
d
-1
d
(u)
arccsc(u) =
2
dx
dx
u √u -1
Regla de la Cadena
d
d
d
(y) =
(y) (u)
dx
du
dx
Definición de Derivada de una Función
d
f(x + ∆x) − f(x)
(y) = lím
∆x→0
dx
∆x
Notaciones de la Derivada
d
d
'
(y) =
f(x) = y' = f (x) = Dx y
dx
dx
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