Tabla Derivadas

1. 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
' )('1upuufp−=
xxfln)(= xxf1)('=
uxfln)(= uuxf')('=
xxfalog)(= axxfln1)('=
uxfalog)(= auuxfln')('=
xexf=)(
xexf=)(
ueuf=)(
' )('ueufu=
xaxf=)(
aaxfxln)(=
uauf=)(
' ln)('uaaufu=
)()()(xhxgxf= ) (' )(ln)()(')( )()()(1)(xhxgxgxgxgxhxfxhxh+=−
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'
xxftg)(= == xxf2cos1)('
x2tg1+=
uxftg)(= == uuxf2cos')('
' )tg1(2uu+=
xxfarcsen)(= 211)(' xxf− =
uxfarcsen)(= 21')(' uuxf− =
xxfarccos)(= 211)(' xxf− − =
uxfarccos)(= 21')(' uuxf− − =
xxfarctg)(= 211)(' xxf+ =
uxfarctg)(= 21')(' uuxf+ =
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'
xxfth )(= == xxf2ch1)('
x2th1−=
uxfth )(= == uuxf2ch')('
' )th1(2uu−=
xxfsh arg)(= 211)(' xxf+ =
uxfsh arg)(= 21')(' uuxf+ =
xxfch arg)(= 11)(' 2− = xxf
uxfch arg)(= 1')(' 2− = uuxf
xxfth arg)(= 211)(' xxf− =
uxfth arg)(= 21')(' uuxf− =