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1. 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 p xxf =)( p∈R 1 )(' − = p pxxf p uuf =)( p∈R ')(' 1 upuuf p− = xxf ln)( = x xf 1 )(' = uxf ln)( = u u xf ' )(' = xxf alog)( = ax xf ln 1 )(' = uxf alog)( = au u xf ln ' )(' = x exf =)( x exf =)( u euf =)( ')(' ueuf u = x axf =)( aaxf x ln)( = u auf =)( 'ln)(' uaauf u = )( )()( xh xgxf = )(')(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 2 cos 1 )(' x2 tg1+= uxf tg)( = == u u xf 2 cos ' )(' ')tg1( 2 uu+= xxf arcsen)( = 2 1 1 )(' x xf − = uxf arcsen)( = 2 1 ' )(' u u xf − = xxf arccos)( = 2 1 1 )(' x xf − − = uxf arccos)( = 2 1 ' )(' u u xf − − = xxf arctg)( = 2 1 1 )(' x xf + = uxf arctg)( = 2 1 ' )(' u u xf + = 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 2 ch 1 )(' x2 th1−= uxf th)( = == u u xf 2 ch ' )(' ')th1( 2 uu−= xxf sharg)( = 2 1 1 )(' x xf + = uxf sharg)( = 2 1 ' )(' u u xf + = xxf charg)( = 1 1 )(' 2 − = x xf uxf charg)( = 1 ' )(' 2 − = u u xf xxf tharg)( = 2 1 1 )(' x xf − = uxf tharg)( = 2 1 ' )(' u u xf − =

Jun. 9, 2020

tabla1

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