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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)( = axxf
ln1)(' = uxf alog)( = au
uxfln
')(' =
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
xf 2cos1)('
x2tg1+=
uxf tg)( = ==u
uxf 2cos')('
' )tg1( 2 uu+=
xxf arcsen)( = 211)('
xxf
−= uxf arcsen)( = 21
')('u
uxf−
=
xxf arccos)( = 211)('x
xf−
−= uxf arccos)( = 21
')('u
uxf−
−=
xxf arctg)( = 211)('x
xf+
= 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 )( = ==x
xf 2ch1)('
x2th1−=
uxf th )( = ==u
uxf 2ch')('
' )th1( 2 uu−=
xxf sh arg)( = 211)('
xxf
+= uxf sh arg)( = 21
')('u
uxf+
=
xxf ch arg)( = 11)('2 −
=x
xf uxf ch arg)( = 1')('
2 −=
uuxf
xxf th arg)( = 21
1)('x
xf−
= uxf th arg)( =
21')('u
uxf−
=