dy f ( x + ∆x ) − f ( x ) = lim dx ∆x →0 ∆x FÓRMULAS FUNDAMENTALES PARA LA DERIVACIÓN DE ALGUNAS FUNCIONES:
d (c ) =0 ( c = constante) dx d (x ) =1 dx d (u ± v ± ... ± w) = du ± dv ± ... ± dw dx dx dx dx d (cu ) du =c dx dx d (uv ) dv du =u +v dx dx dx
( )
d xn = nx n −1 dx
( )
( )
d u du e = eu dx dx d v du dv + u v ln u u = vu v −1 dx dx dx dy dy dv (Regla de la cadena) = ⋅ dx dv dx d (sen u ) = cos u du dx dx d (cos u ) = − sen u du dx dx d (tg u ) = sec2 u du dx dx
( )
d un du = nu n −1 dx dx d u 1 du dv −u = 2 v dx v v dx dx
d (sec u ) = sec u ⋅ tg u du dx dx
d u 1 du = dx c c dx
d (csc u ) = − csc u ⋅ ctg u du dx dx
d dx
( u ) = 2 1u du dx
d dx
( u )=
1
m
m
m −1
(
)
(
)
d du 1 sen −1 u = 2 dx 1 − u dx du dx
m u d (uvz ) = uv dz + uz dv + vz du dx dx dx dx d (ln u ) = 1 du dx u dx
d (log u ) = log e du dx u dx
( )
d (ctg u ) = − csc2 u du dx dx
d u du a = a u ln a dx dx
d du 1 cos −1 u = − 2 dx 1 − u dx d 1 du tg −1 u = dx 1 + u 2 dx d 1 du ctg −1 u = − dx 1 + u 2 dx d 1 du sec −1 u = dx u u 2 − 1 dx
