TABLA DE DERIVADAS

Funciones elementales Funciones compuestas

Función

f(x)

Derivada

f '(x)

Función

f(u) con u = u(x)

Derivada

f '(x) = f '(u).u'(x)

f(x) = k f '(x) = 0

f(x) = x f '(x) = 1

pxxf )( p R 1)(' ppxxf puuf )( p R ' )(' 1upuuf p

xxf ln)( xxf

1)(' uxf ln)( u

uxf

')('

xxf alog)( ax

xfln

1)(' uxf alog)(

au

uxf

ln

')('

xexf )( xexf )( ueuf )( ' )(' ueuf u

xaxf )( aaxf x ln)( uauf )( ' ln)(' uaauf u

)()()( xhxgxf )(' )(ln)()(')( )()( )(1)( xhxgxgxgxgxhxf xhxh

f(x) = sen x f '(x) = cos x f(x) = sen u f '(x) = cos u u'

f(x) = cos x f '(x) = sen x f(x) = cos u f '(x) = sen u u'

xxf tg)( x

xf2cos

1)('

x2tg1

uxf tg)( u

uxf

2cos

')('

' )tg1( 2 uu

xxf arcsen)( 21

1)('

xxf uxf arcsen)( 21

')('

u

uxf

xxf arccos)( 21

1)('

xxf uxf arccos)( 21

')('

u

uxf

xxf arctg)( 21

1)('

xxf uxf arctg)( 21

')('

u

uxf

f(x) = sh x f '(x) = ch x f(x) = sh u f '(x) = ch u u'

f(x) = ch x f '(x) = sh x f(x) = ch u f '(x) = sh u u'

xxf th )( xxf

2ch

1)('

x2th1

uxf th )( u

uxf

2ch

')('

' )th1( 2 uu

xxf sh arg)( 21

1)('

xxf uxf sh arg)( 21

')('

u

uxf

xxf ch arg)( 1

1)('

2xxf uxf ch arg)(

1

')('

2u

uxf

xxf th arg)( 21

1)('

xxf

uxf th arg)( 21

')('

u

uxf

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