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Derivada ln(x)
(Matemática | Cálculo | Derivadas | Tabla de | ln)
(d/dx) ln(x) = 1/x



Demostración de (d-dx) ln(x) : por la definición de e

Dando: La definición de derivadas; La definición de e.
Resuelva:

(d-dx) ln(x) = lim(d->0) [ ln(x+d) - ln(x) ] / d = lim ln((x+d)/x) / d
= lim (1/d) ln(1 + d/x) = lim [ ln (1 + d/x)(1/d) ].

Fije u=d/x y substitua:

lim(u->0) [ ln (1 + u)(1/(ux)) ] = 1/x ln [ lim(u->0) (1 + u)(1/u) ]
= 1/x ln (e) (La definición de e)
= 1/x.

 

  
 
  

 
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