Tabla de derivadas
Derivadas inmediatas Derivadas de logaritmos
f ( x )=k→f ' ( x )=0 f ( x )=ln u→ f '(x )=u 'u
f ( x )=x→f ' (x)=1 f ( x )=logau→ f ' ( x )= u'
u . ln a=u'ulog ae
f ( x )=u± v→f ' ( x )=u'± v ' Derivadas de funciones exponenciales, potenciales
f ( x )=k .u→f ' ( x )=k .u ' f ( x )=au→f ' ( x )=u ' . au . ln a
f ( x )=u . v→f ' ( x )=u' . v+u . v ' f ( x )=eu→f ' (x )=u' . eu .
f ( x )=uv→f ' (x)=u
' . v−u . v 'v2
f ( x )=uv→f ' ( x )=v .uv−1 .u '+uv . v' . ln u
f ( x )= kv→f ' (x)=−k . v '
v2f ( x )=uk→f ' ( x )=k .uk−1 .u '
f ( x )= k
vn→f ' ( x )=−k .n . v '
vn+1Derivadas de una raiz
f ( x )=uk→f ' ( x )=u
'
k;k ≠0 f ( x )= k√u→f ' (x )= u '
k .k√uk−1
Derivadas de funciones trigonometricas Derivadas de funciones trigonometricas inversas
f ( x )=sinu→f '(x )=u' .cosu f ( x )=sin−1u→f ' ( x )= u'
√1−u2
f ( x )=cosu→f ' ( x )=−u ' . sinu f ( x )=cos−1u→f ' ( x )= −u '
√1−u2
f ( x )=tan u→f ' ( x )= u'
cos2u=u ' . sec2u f ( x )=tan−1u→f ' ( x )= u '
1+u2
f ( x )=cot u→ f ' ( x )= u'
sin2u=−u' . csc2u f ( x )=cot−1u→ f ' ( x )= −u'
1+u2
f ( x )=sec u→f ' ( x )=u' .sinucos2u
=u ' . sec u . tan u f ( x )=sec−1u→f ' ( x )= u '
u .√u2−1f ( x )=cscu→f ' ( x )=u
' .cosusin2u
=−u . csc u .cot u f ( x )=csc−1u→ f ' ( x )= −u 'u .√u2−1
Regla de la cadena (para funciones de una variable)
Regla de la cadena (para funciones de dos variables)
(go f )' ( x )=g ' [ f ( x ) ] . f ' ( x ) . x 'z=f (x , y ); x=f (r , s ); y=f (r , s)
∂ z∂ r
= ∂ z∂ x∂x∂ r
+ ∂ z∂ y∂ y∂ r
; ∂ z∂ s
= ∂ z∂ x∂x∂ s
+ ∂ z∂ y∂ y∂ s
Formula de derivada implicita (para funciones de una variable)
Formula de derivada implicita (para funciones de dos variables)
y '=−F ' xF ' y
si f ( x , y , z )=0→ ∂ f∂ x
=−∂ f∂ x∂ f∂ z
;∂ f∂ y
=− ∂ f∂ y∂ f∂ z
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