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)} ].

Set u=d/x and substitute:

lim_(u->0) [ ln (1 + u)^{^(1/(ux))} ] = 1/x ln [ lim_(u->0) (1 + u)^{^(1/u)} ]
= 1/x ln (e) (Definition of e)
= 1/x

This is how you derive the differentiation of ln(x).

Hi, it's been a few days since i came in contact with my blog. There have been a few things going on lately and I'm quite satisfied with the entire of last week. There were no scoldings and generally it was pure slack throughout, with a Good Friday to top it up. Lessons were usual and nothing spectacular happened. I like this kind of slack studying, no need to worry about not handing up homework and all sorts of rubbish projects. So relaxing, especially Sreeni's lesson.

His lesson is practically slack for me. Miss tan's, Mrs Ang's , Mr Wan's , Miss Haiza's and Ms Cheong's also. LOL. I can just say that almost all of the lessons are slack, except Geog. Geog is super boring and I don't like to absorb so much information that my brain feels unnecessary. I'm pretty sure I'm going to push everything into my neurons before the test. I don't like the feeling of having a lack of information.

So long as I can answer any question with ease, school will be relaxing for me.