1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differentiation of ln(x)

  1. May 29, 2009 #1
    1. The problem statement, all variables and given/known data

    I am unsure how to differentiate ln(x).

    2. Relevant equations

    [tex]\int[/tex] dx/ (x logex)

    3. The attempt at a solution

    I let u = logex

    So it became:
    [tex]\int[/tex] x-1u-1dx

    To integrate I now need to find du/dx... which means differentiate ln(x). How does this work out?
  2. jcsd
  3. May 29, 2009 #2


    User Avatar
    Homework Helper

    if y=ln(x) then, x=ey

    find dx/dy. Invert to get dy/dx and then figure out what eln[f(x)] works out to be.
  4. May 29, 2009 #3
    Thanks so much!
  5. May 29, 2009 #4
    Thanks but now I need help on the rest of the question! I'm really stuck. As, when I change it to integral f(x) du, the differentiated ln(x) does not cancel anything out.... Does anyone know how to integrate this equation?

    [tex]\int[/tex] x-1u-1du/e^u

  6. May 29, 2009 #5


    User Avatar
    Homework Helper

    Nothing "cancels" because you're not differentiating log(x) correctly. I don't really know how you can encounter these kind of problems without ever having seen the derivative of log(x), but this is how it works.

    y=\log x \Rightarrow x=e^y, \;\;
    \frac{dx}{dx}=\frac{d e^y}{dx}=e^y \frac{dy}{dx}=1 \Rightarrow \frac{dy}{dx}=\frac{1}{e^y} \Rightarrow \frac{d log x}{dx}=\frac{1}{x}[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook