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?