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Formulas to find any derivative
Typology: Cheat Sheet
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Derivada de una función en un punto:
tgα=
f ( a+h)−f (a)
h
m=lim
h → 0
f ( a+h)−f ( a)
h
f ' (a)=lim
h → 0
f ( a+ h)−f (a)
h
Ecuación recta – tangente:
y=f
'
( a) ( x−a) +f (a)
Ecuación normal:
y=
f
'
a
( x−a )+ f ( a)
Derivadas laterales:
f
'
f
'
*Si las derivadas laterales coinciden f es derivable en a y si no coinciden, f no es
derivable en a.
Definición de derivada:
f ' ( x)=lim
h → 0
f ( x +h)−f (x )
h
f(x) f’(x)
k 0
x
n
nx
n− 1
f ( x ) ± g ( x) f ’ ( x )± g ’ (x )
[f ( x ) ]
2
2 f ( x ) f '( x )
f (x) ∙ g (x) f
'
( x ) g ( x ) +f ( x ) g ' (x)
f ( x )
g ( x)
f
'
x
g
x
−f
x
g ' (x)
[g
x
2
f (x)
f ' (x )
[f ( x ) ]
a
a [f ( x )]
a− 1
f ' ( x)
(f ∘ g)' ( x) f
'
x
ln x
x
ln f ( x)
f ' ( x )
f ( x )
log
a
x
ln a
x
log
a
[f ( x )]
ln a
f ' (x )
f (x )
e
x
e
x
a
x
ln a ∙ a
x
sen x cos x
cos x −sen x
tg x
cos
2
x
= 1 +tg
2
x
arc sen x
1 −x
2
arccos x
1 −x
2
