Download - Tabla de Derivadas
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