derivada del logaritme

d_{x}[x] = 1
d_{x}[e^{ln(x)}] = 1
d_{ln(x)}[e^{ln(x)}]·d_{x}[ln(x)] = 1
e^{ln(x)}·d_{x}[ln(x)] = 1
x·d_{x}[ln(x)] = 1
d_{x}[ln(x)] = (1/x)


d_{x}[x+a] = 1
d_{x}[e^{ln(x+a)}] = 1
d_{ln(x+a)}[e^{ln(x+a)}]·d_{x}[ln(x+a)] = 1
e^{ln(x+a)}·d_{x}[ln(x+a)] = 1
(x+a)·d_{x}[ln(x+a)] = 1
d_{x}[ln(x+a)] = ( 1/(x+a) )


d_{x}[x^{n}] = nx^{(n+(-1))}
d_{x}[e^{ln(x^{n})}] = nx^{(n+(-1))}
d_{ln(x^{n})}[e^{ln(x^{n})}]·d_{x}[ln(x^{n})] = nx^{(n+(-1))}
e^{ln(x^{n})}·d_{x}[ln(x^{n})] = nx^{(n+(-1))}
x^{n}·d_{x}[ln(x^{n})] = nx^{(n+(-1))}
d_{x}[ln(x^{n})] = (1/x^{n})·nx^{(n+(-1))}
d_{x}[ln(x^{n})] = (n/x)