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