Proof of the derivative of ln(x)

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Question description

I'm trying to prove that ddxlnx=1x.

Here's what I've got so far:


To simplify the logarithm:


^This is the line I have trouble with. I can see that it is true by putting numbers in, but I can't prove it. I know that e1x=limh→0(1+h)1xh, but I can't work out how to get from the above line to that.


Going back to the derivative:


This proof seems fine, apart from the middle step to get e1x. How could I prove that part?

Tutor Answer

(Top Tutor) Daniel C.
School: University of Virginia
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