ddxc=0ddx ( x

n

c )=nc xn−1ddx ( x

n

xm )=(n−m ) x[n− (m+1 )]ddx ( ln x

n

xm )= 1xm+1

(n−m ln xn)

ddx √c=0d

dx √u= 12√u

dudx

ddx ( u√ xv )=u( 1

2√x−√xvdudx )d

dxloga √u=

12u ln a

dudx

ddxx=1ddxun=nun−1 du

dxddxuvw=uv dw

dx+uw dv

dx+vw du

dxddxsen (u )=cos (u ) du

dxddxcx=cddx

cun=cnun−1 dudx

ddxu+v−w=du

dx+ dvdx

−dwdx

ddxcos (u )=−sen (u ) du

dxddxcu=c du

dxddx

(uv )=u dvdx

+v dudx

ddx (√u√v )= 1

2√v ( 1√u dudx−√uvdvdx )

ddxtan (u )=sec2 (u ) du

dx

ddxx+c=xddx

(u−v )= dudx

− dvdx

ddxln (x+√u )= 1

x+√u (1+ 12√u

dudx )d

dxcot (u )=−csc2 (u ) du

dxddx √ x= 1

2√ xddx

(u+v )= dudx

+ dvdx

ddx (√uxn )= 1

xn ( 12√u

−n√ux )d

dxsec (u )=sec (u ) tan (u ) du

dxddxu=dudx

ddx ( cu )=−c

u2dudx

ddxln( c+√u

x )= 12 (c √u+u )

dudx

−1x

ddxcsc (u )=−csc (u ) cot (u ) du

dxddx ( xc )=1cddx ( c√ x )= −c

22√x3

ddx (√ x√u )= 1

√u ( 1√ x−√ xududx )d

dxarcsen (u )= 1

√1−u2dudx

ddxxn=nxn−1ddx ( c√u )= −c

2√u3dudx

ddx (√uv )= 1

2v √ududx

−√uv2dvdx

ddxarccos (u )=− 1

√1−u2dudx

ddxcxn=cnxn−1ddx

(u√x )=√x dudx +u2√x

ddx ( xcu )= 1

cu (1− x ln (c ) dudx )

ddxarctan (u )= 1

1+u2dudx

ddx ( x

n

n )=xn−1ddx ( ux )=1x ( dudx−ux )d

dx ( cm√ xn )=

−cnmx(− (m+n )

m )ddxarc cot (u )=− 1

1+u2dudx

ddxex=e xddx ( x√u )= 1

√u (1− xu dudx )ddx

(u√v )= u2√v

−√v dudxddxarc sec (u )= 1

u√u2 − 1dudx

ddxeu=eu du

dxddx ( uxn )= 1

x2 (dudx−

nux )d

dx ( un

vm )= unvm ( nu dudx−mv dvdx )ddxarc csc (u )=− 1

u√u2−1dudx

ddx ( uc )=1c dudxddx

(xnm )= nm x

(n−mm )ddxcxnln (u )= c

xn (1ududx

−nxln (u ))d

dxsenn (u )=ncos (u ) sen (n−1 ) (u ) du

dx

ddx ( cxn )=−cn

xn+1ddxcuv=cu dv

dx+cv du

dxddxu ln (v )=u

vdvdx

+ ln ( v ) dudx

ddxsenn (u )=ncot (u ) senn (u ) du

dxddx ( √ xc )= 1

2c√ xddx

(m√un )= nm√u (n−m )

mdudx

ddx ( cm√un ) ¿

−cn

mm√un+mdudx

ddxcosn (u )=−nsen (u ) cos(n−1 ) (u ) du

dx

ddxln (u )=1

ududx

ddx

(m√un )= n

m m√u(m−n )

dudx

ddxarcvers (u )= 1

√2 v−v2dudx

ddxcos (u )=−n tan (u ) cosn (u ) du

dx

ddxln (xn)=n

xddx

u√v

= 1√vdudx

− u2√v3

dvdx

ddxu ln ( x )=u

x+ln ( x ) du

dxddxtann (u )=nsec2 (u ) tan(n−1 ) (u ) du

dx

ddxx ln ( x )=1+ ln xddxln (uv )=1

vdvdx

+1ududx

ddx ( √u

cxn )= 1cxn ( 1

2√ududx

− n√ux )d

dxtann (u )=n tann (u )csc (u ) sec (u ) du

dx

ddxx ln ( c )=ln cddx ( uv )=1v dudx− u

v2dvdx

ddx ( c

u

av )= cu

av ( ln (c ) dudx

− ln (a ) dvdx )

ddxtann (u )=ncsc2 (u ) tan(n+1 ) (u ) du

dx

ddxloga cx

n= nx ln a

ddxln( uv )= 1u dudx− 1v dvdxddxlogc (uv )= 1

ln c ( 1u dudx−1v dvdx )ddxcotn (u )=−ncsc2 (u ) cot (n−1 ) (u ) du

dx

ddxloga x

n= nx ln a

ddx

(c√u)= c√n

2√uln ( c ) du

dxddxcuav=cuav( ln (a ) dv

dx+ln (c ) du

dx )ddxcotn (u )=n sec2 (u ) cot(n+1 ) (u ) du

dx

dydx

=dydududvdvdx

ddx

x√u

= 1√u

− x2√u3

dudx

ddxln(√ uv )=12 ( 1u dudx−1v dvdx )ddxcotn (u )=ncotn (u ) sec (u ) csc (u ) du

dx

ddx (√cxn )=−n√c

xn+1ddxln ( x )x

= 1xn

(1−ln ( x ) )ddxlogc ( lnu )= 1

u ( ln c ) ( lnc )dudx

ddxsecn (u )=n secn (u ) tan (u ) du

dx

ddx ln ( cxn )=−

nx

ddx (√ xv )=1v ( 1

2√x−√xvdvdx )d

dxuv=vuv−1 du

dx+uv ln (u ) dv

dxddxcscn (u )=−ncscn (u ) cot (u ) du

dx

ddx (uv )=

v dudx

−u dvdx

v2

ddxx ln (u )= x

ududx

+ ln xddxlogc ( ux )= 1

ln c ( 1u dudx−1x )ddxln m√( uv )

n= nm ( 1u dudx−1v dvdx )

ddxu ln (c )= ln ( c ) du

dxddx ( c

u

xn )= cu

xn (ln (c ) dudx

−nx )d

dx (m√unc )=nm√un−mcm

dudx

ddx ( ln x

n

xm )= 1xm+1

(n−m ln xn)

ddxlogc x=

1x ln c

ddxLoga=

Logaeu

dudx

ddxloga( uvc )= 1

ln a ( 1u dudx + 1vdvdx )d

dxln ( logcu )= 1

u ln ududx

ddxcu=cu ln (c ) du

dxddxLogau=

1u ln (a )

dudx

ddx ( uln v )=( dudx− u

v ln vdvdx )d

dxloga ( u√vc )= 1

ln a (1u dudx + 12v dvdx )

ddx logc ( uxn )= 1

ln c ( 1u dudx−nx )