TEMA 4. FUNCIÓN REAL DE VARIABLE REAL Tabla de derivadas f (x) x m f '( x ) mx m 1 f ( x ) u( x )m f '( x ) mu( x )m 1 u '( x ) f ( x ) ax con a > 0 f '( x ) ax ln a f ( x ) au( x ) con a > 0 f '( x ) au( x ) ln a u '( x ) f (x) e x f '( x ) e x f ( x ) eu( x ) f '( x ) eu( x )u '( x ) f ( x ) loga x con a > 0 f ( x ) loga u( x ) con a > 0 f ( x ) ln x f ( x ) ln u( x ) f ( x ) senx 1 x u '( x ) f '( x ) u( x ) f '( x ) cos x f ( x ) senu( x ) f '(x ) cos u( x ) u '(x ) f ( x ) cos x f '( x ) senx f ( x ) cosu( x ) f '( x ) -senu( x ) u '( x ) f ( x ) tgx f '(x ) f ( x ) tgu(x ) f '( x ) f ( x ) cotgx f '(x ) f ( x ) cotgu(x ) f ( x ) arcsenx f '(x ) f ( x ) arcsenu(x ) f '( x ) f ( x ) arccos x f '(x ) f ( x ) arccosu( x ) f '( x ) f ( x ) arctgx f '( x ) f ( x ) arctgu( x ) f '(x ) f ( x ) arccotgx f ( x ) arccotgu(x ) 1 1 1 loga e ln a x x 1 1 u '( x ) f '(x ) loga e u '( x ) u( x ) ln a u( x ) f '( x ) f '( x ) 1 2 1 tg2 x cos x u '(x ) cos2 u(x ) 1 1 tg2u( x ) u '(x ) 1 cotg2 x sen2 x u '( x ) f '( x ) 1 cotg2u( x) u '( x) 2 sen u( x ) f '( x ) f '(x ) 1 1 x2 u '( x ) 1 u( x )2 1 1 x2 u '( x ) 1 u( x )2 1 1 x2 u '( x ) 1 u( x )2 1 1 x2 u '( x ) 1 u( x )2