1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Derivative of 1 / ln x

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of 1 / ln x

    2. Relevant equations

    N/A

    3. The attempt at a solution

    y = 1/lnx

    First Attempt:
    y' = -1/x/(lnx)^2
    y' = -1 / x(lnx)^2

    Second Attempt:
    ln y = ln (1 / lnx)
    ln y = ln 1 - ln x
    ln y = -lnx
    dy/dx = y(-1/x)
    dy/dx = -1/xlnx

    Third Attempt:
    ln y = -lnx
    y = -x
    y' = -1

    Which one is it? =/
     
  2. jcsd
  3. Oct 28, 2007 #2

    rock.freak667

    User Avatar
    Homework Helper

    In your second attempt this step is wrong
    ln y = ln (1 / lnx)
    ln y = ln 1 - ln x

    It should be lny=ln 1 -ln(lnx)
     
  4. Oct 28, 2007 #3
    We know the derivative would be the denominator times the derivative of the numerator(which would be zero in this case), minus the numerator times the derivative of the denominator(which is 1/x), over the denominator squared.
     
  5. Oct 28, 2007 #4

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Use the product rule. Sure you can do the quotient rule but the product rule is so easy to remember!
     
  6. Oct 28, 2007 #5
    What made you doubt your first attempt? Using the product rule:

    [tex]\frac{d}{{dx}}\left( {\frac{1}{{\ln x}}} \right) = \frac{{0 \cdot \ln x - 1\left( {\frac{1}{x}} \right)}}{{\left( {\ln x} \right)^2 }} = \frac{{ - \frac{1}{x}}}{{\left( {\ln x} \right)^2 }} = - \frac{1}{{x\left( {\ln x} \right)^2 }}[/tex]
     
  7. Oct 29, 2007 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    That isn't the product rule!

    What JasonRox meant, I think, was use the chain rule on (ln x)-1.
     
  8. Oct 29, 2007 #7
    Your first approach was correct, the second one, as already pointed, instead of ln(lnx) you took lnx.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Derivative of 1 / ln x
  1. Converge of 1/ln(x) (Replies: 14)

  2. Integral of 1/ln(x) (Replies: 6)

  3. Derivative of ln(ln x) (Replies: 4)

Loading...