ddx

(c )=0

ddx

( x )=1

ddx

(xn )=nxn−1

ddx

[cf ( x )]=cf '(x )

ddx

[ f ( x )±g ( x ) ]=f ' ( x )±g '( x)

ddx

[ f ( x )g ( x ) ]=f ( x )g' ( x )+g ( x ) f ' (x )( producto)

ddx [ f (x )g(x) ]= g ( x ) f ' ( x )−f (x )g '( x)

[ g(x) ]2(cociente)

ddxf (g (x))=f ' (g ( x ) ) g' ( x )(regla de lacadena)

ddx

(ex )=ex

ddx

(ax )=ax ln a

ddxln|x|=1

x

ddx

( loga x )= 1x ln a

ddx

( sen x )=cos x

ddx

(cos x )=−sen x

ddx

( tan x )=sec2 x

ddx

(csc x )=−csc x cot x

ddx

( sec x )=sec x tan x

ddx

(cot x )=−csc2 x

ddx

( sen−1 x )= 1

√1−x2

ddx

(cos−1 x )= −1

√1+x2

ddx

( tan−1 x )= 1

1+x2

ddx

(csc−1 x )= −1x √x2−1

ddx

( sec−1 x )= 1

x √x2−1ddx

(cot−1 x )= −11+x2

log a ( xy )=loga x+ loga y

log a( xy )= loga x− loga ylog a (xr )=r loga x