Derivadas

TABLA DE DERIVADAS TABLA DE DERIVADAS
FUNCIÓN FUNCIÓN DERIVADA FUNCIÓN FUNCIÓN DERIVADA

a
x

0

sen xsen u

cos x
u' cos u

1
2x m � x m�1

x2

cos x cos u

� senx
� u' senu

xm

f ( x ) � g( x)
k.f(x) f ( x ) � g( x )
f (x) g( x ) 1 f(x)

f ' ( x ) � g' ( x )
k.f' (x) f ' ( x ) � g( x ) � f ( x )� g' ( x )
f ' ( x ) � g( x ) � f ( x ) � g' ( x ) g2 ( x ) � f ' (x) f 2 (x)
f ' �g�x �� � g' �x �

tgxtgu cot gx
cot g u
sec x

1 � 1 � tg 2 x 2 cos x u' cos 2 u �1 � �(1 � cot g 2 x ) 2 sen x � u' � �(1 � cotg 2u) � u' 2 sen u
tg x � sec x u' � tg u � sec u � cot g x � cos ec x

�f � g�( x )
um

sec u cos ec xm � um�1 � u' 1 x u' u ln x ln a 1 x ln a u' u ln a ex u' e u a x . ln a a u .ln a u' v.u' � � u v � v' ln u� � u � �

ln x
ln u lga x � lga u ex eu ax au uv

cos ec u
arc sen x
arc sen u

� u'� cot g u � cosec u
1 1� x 2 u'
1� u2 �1 1� x 2 � u' 1� u2 1 1� x 2 u' 1� u2 �1 1� x 2 � u' 1� u2

arc cos x arc cos uarc tg x arc tg u arc ctg x arc ctg u

a,k ,m son constantes

u,v,f,g,son funciones de la variable x