TABLA DE DERIVADAS

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 f (x) = x p∈R 1 '( ) − = p f x px p f (u) = u p∈R '( ) ' 1 f u pu u p− = f (x) = ln x x f x 1 '( ) = f (x) = ln u u u f x ' '( ) = f x x a ( ) = log x a f x ln 1 '( ) = f (x) = loga u u a u f x ln ' '( ) = x f (x) = e x f (x) = e u f (u) = e f '(u) e u' u = x f (x) = a f x a a x ( ) = ln u f (u) = a f '(u) a ln a u' u = ( ) ( ) ( ) h x f x = g x ( ) ( ) ( ) '( ) ( ) ln ( ) '( ) ( ) 1 ( ) f x h x g x g x g x g x h x h x h x = + − 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' f (x) = tg x = = x f x 2 cos 1 ' ( ) x 2 = 1+ tg f (x) = tg u = = u u f x 2 cos ' ' ( ) (1 tg ) ' 2 = + u u f (x) = arcsen x 2 1 1 '( ) x f x − = f (x) = arcsenu 2 1 ' '( ) u u f x − = f (x) = arccos x 2 1 1 '( ) x f x − − = f (x) = arccosu 2 1 ' '( ) u u f x − − = f (x) = arctg x 2 1 1 '( ) x f x + = f (x) = arctgu 2 1 ' '( ) u u f x + = 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' f (x) = th x = = x f x 2 ch 1 ' ( ) x 2 = 1− th f (x) = th u = = u u f x 2 ch ' ' ( ) (1 th ) ' 2 = − u u f (x) = argsh x 2 1 1 '( ) x f x + = f (x) = argsh u 2 1 ' '( ) u u f x + = f (x) = arg ch x 1 1 '( ) 2 − = x f x f (x) = arg ch u 1 ' '( ) 2 − = u u f x f (x) = arg th x 2 1 1 '( ) x f x − = f (x) = arg th u 2 1 ' '( ) u u f x − =