RESUMEN DE FORMULAS DE DERIVACIÓN
3
REGLAS PARA DERIVAR FUNCIONES ALGEBRAICAS I. d dx ( c)=0 II. d dx ( x)=1 Ia d dx ( kx)=k IIa d dx ( x n )=nx n−1 IIIa d dx ( kx n ) =knx n−1 III. d dx ( u−v + w )= d dx ( u)+ d dx ( v)− d dx ( w ) IV. d dx ( cv)=c d dx ( v) V. d dx ( uv )=u d dx ( v ) +v d dx ( u) VI. d dx ( v n )=nv n−1 d dx ( v ) VIa. d dx ( n √ u )= d dx ( u) n √ u n−1 VII. d dx ( u v ) = v du dx −u dv dx v 2
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Transcript of RESUMEN DE FORMULAS DE DERIVACIÓN
REGLAS PARA DERIVAR FUNCIONES ALGEBRAICAS
I.ddx
(c)=0
II.ddx
(x )=1
Iaddx
(kx)=k
IIaddx
(xn )=nxn−1
IIIaddx
(kxn )=kn xn−1
III.ddx
(u−v+w )= ddx
(u)+ ddx
(v )− ddx
(w)
IV.ddx
(cv)=c ddx
(v )
V.ddx
(uv )=u ddx
( v )+v ddx
(u)
VI. ddx
(vn )=n vn−1 ddx
(v )
VIa. ddx
( n√u )=
ddx
(u)
n√un−1
VII. ddx ( uv )=
vdudx
−u dvdx
v2
VIIa. ddx ( vc )=
ddx
(v)
c
VIIb. ddx ( cv )=
−c ddx
(v)
v2
VIII. dydx=dydv . dvdx , siendo y funciónde v .IX.
dydx
= 1dxdy
, siendo y funciónde x
REGLAS PARA DERIVAR FUNCIONES TRASCENDENTES
X. ddx
(ln v )=
ddx
(v )
v=1vdvdx
(ln v=loge v )
Xaddx
(log v )= log evdvdx
XI.ddx
(av )=av ln a dvdx
XIa.ddx
(ev )=ev dvdx
XII.ddx
(uv)=vuv−1 dudx
+ ln u .uv dvdx
XIII.ddx
( senv )=cosv dvdx
XIV.ddx
(cos v )=−senv dvdx
XV.ddx
( tan v )=sec2 v dvdx
XVI. ddx (cot v )=−csc2 v dvdx
XVII.ddx
( sec v )=sec v tan v dvdx
XVIII.ddx
(csc v )=−csc v cot v dvdx
XIX.ddx
(vers v )=senv dvdx
XX. ddx
(arc senv )=
dvdx
√1−v2
XXI. ddx
(arc cos v )=−dvdx
√1−v2
XXII. ddx
(arc tan v )=
dvdx
1+v2
XXIII. ddx
(arc cot v )=−dvdx
1+v2
XXIV. ddx
(arc sec v )=
dvdx
v√v2−1
XXV. ddx
(arc csc v )=−dvdx
v √v2−1
XXVI. ddx
(arc vers v )=
dvdx
√2v−v2
