(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to prove that d ln(x) / dx = 1/x

This isn't a homework problem of mine for any class. I'm just doing it for fun, so if I'm faced with something I'm not sure of, I apologize. I've only made it through Calculus 2

3. The attempt at a solution

Difference quotient

ln(x+h)-ln(x) / h

ln([x+h]/x) / h

ln(1+[h/x]) * 1/h

u = h/x So limit h-->0 becomes limit u--> 0

ln(1+u) * 1/ux = 1/x * ln[(1+u)^(1/u)]

Here's where I stopped. A friend of mine told me the ln[(1+u)^(1/u)] as u approaches 0 = ln(e) which makes sense, and I believe he said it was a known identity. Can anyone prove this fact to me?

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# Homework Help: Finding derivative of ln(x)

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