TAULA DE DERIVADES

f (x) f ’ (x) = D f (x)

k (constant) 0

x p p · x p–1

e x e x

a x a x · ln a

ln x

log a x

sin x cos x

cos x – sin x

tg x 1 + tg 2 x =

arc sin x

arc cos x

arc tg x

Regles de derivació

H (x) H ’ (x)

k · f(x) k · f ’ (x)

f (x) g (x) f ’ (x) g ’ (x)

f (x) · g (x)f ’ (x) · g (x) + f (x) · g ’ (x)

( f º g ) (x) = f ( g (x) )f ’ ( g(x) ) · g ’ (x)

f –1 (x)

1f ’ ( f –1 (x) )

f (x)g (x)

f ’ (x) · g (x) – f (x) · g ’ (x)( g (x) ) 2