Funciones y derivadas

DERIVADAS
FUNCIONES
f ( x) = k
f ' ( x) = 0
f ( x) = x
f ' ( x) = 1
f ( x ) = g ( x ) + h( x )
f ' ( x ) = g ' ( x ) + h' ( x )
f ( x ) = g ( x )·h( x )
f ' ( x ) = g ' ( x )·h( x ) + g ( x )·h' ( x )
f ( x) =
g ( x)
h( x )
f ' ( x) =
f ( x) = x n
g ' ( x )·h( x ) − g ( x )·h' ( x )
[h( x )]2
f ' ( x ) = nx n −1
f ( x ) = [g ( x )]
f ' ( x ) = n[g ( x )]
f ( x) = x
f ' ( x) =
n
f ( x ) = n g ( x ) = [g ( x )]n
1
f ( x) = a x
f ( x) = a g ( x )
f ( x) = e g ( x )
n−1
·g ' ( x )
1
2 x
1
1
−1
f ' ( x ) = ·[g ( x )]n ·g ' ( x )
n
f ' ( x ) = a x ·ln a
f ' ( x ) = a g ( x ) ·ln a·g ' ( x )
f ' ( x ) = e g ( x ) ·g ' ( x )
f ( x ) = ln x
f ' ( x) =
1
x
f ( x ) = ln g ( x )
f ' ( x) =
g ' ( x)
g ( x)
f ( x ) = log a x
f ' ( x) =
1
1
log a e =
x
x ln a
f ( x ) = log a g ( x )
f ' ( x) =
g ' ( x)
g' ( x)
log a e =
g ( x)
g ( x ) ln a