danielatha4
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Homework Statement
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
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?