Tabla De Derivadas

Tabla de Derivadas f ( x ) ............................................ f ′ ( x ) k ..................................................0 x n ................................................ nx n − 1 1 ln x .............................................. x g′( x) ln  g ( x )  ........................................ g x

( ) g ( x ) ± h ( x ) ................................. g ′ ( x ) ± h ′ ( x ) g ( x ) ⋅ h ( x ) ................................... g ′ ( x ) ⋅ h ( x ) + g ( x ) ⋅ h ′ ( x ) g ( x) g ′ ( x ) ⋅ h ( x ) − g ( x ) ⋅ h′ ( x ) ........................................... 2 h ( x)  h ( x )  g x g x e ( ) ..............................................g ′ ( x ) ⋅ e ( ) k x ................................................ k x ⋅ ln k k

g( x)

.............................................ln k ⋅ g ′ ( x ) ⋅ k

log b ( x ) ..........................................

log b ( e )

log b  g ( x )  ....................................  g ( x ) 

h( x )

g( x)

x g ′ ( x ) ⋅ log b ( e ) g ( x)

....................................h′ ( x )  g ( x ) 

g( x)

h( x )

 g ( x )  .................................... g ′ ( x )  g ( x )  x x .................................................... x x ( ln x + 1)

⋅ ln  g ( x )  + h ( x )  g ( x ) 

g( x)

⋅ ln  g ( x )  + g ′ ( x )  g ( x ) 

sen ( g ( x ) ) ........................................cos ( g ( x ) ) ⋅ g ′ ( x )

cos ( g ( x ) ) ....................................... − sen ( g ( x ) ) ⋅ g ′ ( x ) tg ( g ( x ) ) ..........................................sec 2 ( g ( x ) ) ⋅ g ′ ( x )

cotg ( g ( x ) ) ....................................... − csc2 ( g ( x ) ) ⋅ g ′ ( x )

sec ( g ( x ) ) .........................................sec ( g ( x ) ) ⋅ tg ( g ( x ) ) ⋅ g ′ ( x )

csc ( g ( x ) ) ......................................... − csc ( g ( x ) ) ⋅ cotg ( g ( x ) ) . g ′ ( x ) arcsen ( g ( x ) ) ....................................

g′( x)

1− ( g ( x))

2

h ( x ) −1

⋅ g′( x)

g( x)

arccos ( g ( x ) ) .................................... arctg ( g ( x ) ) ...................................... arccotg ( g ( x ) ) ..................................

−g′( x) 1− ( g ( x)) g ′( x)

1+ ( g ( x ))

arccsc ( g ( x ) ) ....................................

2

−g′( x)

1+ ( g ( x ))

arcsec ( g ( x ) ) ....................................

2

2

g′( x)

( g ( x ))

g ( x)⋅

2

−1

−g′( x)

( g ( x ) ) −1 senh ( g ( x ) ) ......................................cosh ( g ( x ) ) ⋅ g ′ ( x ) cosh ( g ( x ) ) ......................................senh ( g ( x ) ) ⋅ g ′ ( x ) tgh ( g ( x ) ) ........................................sech ( g ( x ) ) ⋅ g ′ ( x ) cotgh ( g ( x ) ) .................................... − csch ( g ( x ) ) ⋅ g ′ ( x ) sech ( g ( x ) ) ...................................... − sech ( g ( x ) ) ⋅ tgh ( g ( x ) ) ⋅ g ′ ( x ) csch ( g ( x ) ) ...................................... − csch ( g ( x ) ) ⋅ cotgh ( g ( x ) ) ⋅ g ′ ( x ) g ( x)⋅

2

2

2

arg senh ( g ( x ) ) ................................. arg cosh ( g ( x ) ) ................................

arg tgh ............................................

1+ ( g ( x ))

arg sech ( g ( x ) ) ............................... arg csch ( g ( x ) ) ...............................

2

g′( x)

( g ( x ))

2

−1

g′( x)

1− ( g ( x))

arg cotgh ( g ( x ) ) .............................

Lic. Eleazar J. García

g′( x)

2

−g′( x)

1+ ( g ( x ))

2

−g′( x)

g ( x ) ⋅ 1− ( g ( x ))

2

−g′( x) g ( x ) ⋅ 1+ ( g ( x ) )

2

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