Tabla de derivadas de funciones compuestas.
Supongamos que u= f(x).
Función Derivada
y= uk ⋅ y’= 'uk ⋅
y= n
u y’= '
1unun⋅
−
y= u y’= '
2
1u
u
⋅
y=ln u y’= '
1u
u
⋅
y= u
1 y’= '
1
2u
u
⋅
−
y= u
e y’= 'ueu⋅
y= u
a y’= ')(ln uaau⋅⋅
y= )(usen y’= ')(cos_ uu
⋅
y= )cos(u y’= ')_( uusen
⋅
−
y= )(utag y’= =⋅+ ')1( 2uutag
'
cos
1
2u
u
⋅
y= )(uarcsen y’= '
1
1
2u
u
⋅
−
y= )arccos(u y’= '
1
1
2u
u
⋅
−
−
y= )(uarctag y’= '
1
1
2u
u
⋅
+
y= u
a
log y’= '
ln
11 u
au
⋅⋅
Reglas de derivación.
y= f ±g y’= f ´
±
g´
y= f • g y’= f ´• g + f • g´
y= g
f y’= 2
´´
g
gfgf
⋅
−
⋅
Regla de la cadena
y= g(f(x))
y’= g´(f(x)) • f ´(x)