Tabla de Derivadas e Integrales

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Tabla de Derivadas e Integrales Powered By Docstoc
					                            A TODA HORA TU CLASE
                           CLASES DE LUNES A LUNES
                            PROFESORES DE LA UBA
                                  4788-0081

                Tabla de Derivadas e Integrales
   Función                              Derivadas                          Integrales
y=c               y' = 0                                  c.x
                                                                  2
y = c.x           y' = c                                  c.x /2
      n                        n-1                            n+1
y=x               y' = n.x                                x         /n+1
      -n                                 n-1                   n+1
y=x               y’ = -1/(n.x )                          x-          /-n+1
      ½                                 ½                         3/2
y=x               y’ = 1/(2.x )                           2.x /3
      a/b                      (a/b)-1                        (a/b)+1
y=x               y' = a.x                   /b           x             /[(a/b)+1]
                                2
y = 1/x           y' = -1/x                               ln x
y = sen x         y' = cos x                              -cos x
y = cos x         y' = -sen x                             sen x
                                     2
y = tg x          y' = 1/cos x                            -ln cos x
                                         2
y = cotg x        y' = -1/sen x                           ln sen x
                                                  2
y = sec x         y' = sen x/cos x                        ln (tg ½.x)
                                                  2
y = cosec x       y' = -cos x/sen x                       ln [cos x/(1 - sen x)]
                                            2 ½                                      2 ½
y = arcsen x      y' = 1/(1 - x )                         x.arcsen x + (1 - x )
                                             2 ½                                     2 ½
y = arccos x      y' = -1/(1 - x )                        x.arccos x - (1 - x )
                                             2                                             2
y = arctg x       y' = 1/(1 + x )                         x.arctg x - ½ln (1 + x )
                                              2                                                2
y = arccotg x     y' = -1/(1 + x )                        x.arccotg x + ½ln (1 + x )
                                        2         ½
y = arcsec x      y' = 1/[x.(x -1) ]
                                         2            ½
y = arccosec x    y' = -1/[x.(x – 1) ]
y = senh x        y' = cosh x                             cosh x
y = cosh x        y' = senh x                             senh x
                                    2
y = tgh x         y' = sech x                             ln cosh x
                                             2
y = cotgh x       y' = -cosech x                          ln senh x
y = sech x        y' = -sech x.tgh x
y = cosech x      y' = -cosech x.cotgh x
y = ln x          y' = 1/x                                x.(ln x - 1)
y = logax         y' = 1/x.ln a                           x.( logax - 1/ln a)
      x                    x                                  x
y=e               y' = e                                  e
      x                    x                                  x
y=a               y' = a .ln a                            a /ln a
      x                    x
y=x               y' = x .(ln x + 1)
      u                    u
y=e               y’ = e .u’
y = u.v           y' = u'.v + v'.u                        u.dv + v.du
                                                      2
y = u/v           y' = (u'.v - v'.u)/v
      v                    v
y=u               y' = u .(v'.lnu + v.u'/u)
                  A TODA HORA TU CLASE
                 CLASES DE LUNES A LUNES
                  PROFESORES DE LA UBA
                        4788-0081
                                           2
y = lnuv   y’ = (v’.u.lnu - u’.v.lnv)/v.u.ln u