Creating a function that derives the function `Log[x]`

Question

I want to create a function that derives (Derivada) the function Log[x] for any base.

My code:

Derivada[x_^n_, x_Symbol] /; FreeQ[n, x] := n*x^(n - 1)
Derivada[n_*x_, x_Symbol] /; FreeQ[n, x] := n
Derivada[Log[a_: E, x_], x_Symbol] := 1/(x*Log[a])
Derivada[f_, x_Symbol] /; FreeQ[f, x] := 0
Derivada[(a_?NumericQ) f_, x_Symbol] := a*Derivada[f, x]
Derivada[Exp[x_], x_Symbol] := Exp[x]
Derivada[a_^x_, x_Symbol] := a^x Log[a]
Derivada[u_Plus, x_Symbol] := Derivada[#, x] & /@ u
Derivada[u_*v_, x_Symbol] := u Derivada[v, x] + v Derivada[u, x]
Derivada[u_/v_, x_Symbol] := (Derivada[u, x]*v - u*Derivada[v, x])/v^2

My problem is to derive Log[x]. The functions works for any base Log[2,x], Log[3,x] except when I use just Log[x].

Doesn't work:

In[64]:= Derivada[Log[x], x]

Out[64]= Derivada[Log[x], x]

Works:

In[65]:= Derivada[Log[2, x], x]

Out[65]= 1/(x Log[2])

Answer 1

Just add the rule

Derivada[Log[x_], x_Symbol] := 1/x

Since Log[x] has only one argument, it cannot match with the pattern Derivada[Log[a_: E, x_] - even if the first argument is optional:

MatchQ[Log[a_: E, x_], Log[x]]

False