Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Need some help differentiating

  1. Mar 28, 2008 #1
    [SOLVED] need some help differentiating

    Uh my bad, forgot how to differentiate ln's


    1. The problem statement, all variables and given/known data
    [tex]\frac{V_0}{xln(\frac{b}{x})} [/tex]
    Find dE/dx

    I can almost get the answer, but I had to use matlab to find the actual answer, so I am kind of feeling stupid now.

    My problem is when I try to differentiate the ln

    2. Relevant equations



    3. The attempt at a solution

    [tex]d/dx(\frac{V_0}{xln(\frac{b}{x})}) = \frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b/x^2}{x ln(b/x)^2} =[/tex]

    [tex]\frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b}{x^3 ln(b/x)^2}[/tex]

    The second term should only have x^2 in it (and no b), does anyone see where I went wrong?
     
    Last edited: Mar 28, 2008
  2. jcsd
  3. Mar 28, 2008 #2
    [tex]log_a(x)=y=>a^{y}=x[/tex] let's differentiate this implicitly, we get:

    [tex]\frac{d}{dx}(a^{y}=x)=>\frac{dy}{dx}a^{y}lna=1=>\frac{dy}{dx}=\frac{1}{a^{y}lna}=>\frac{dy}{dx}=\frac{1}{xlna}[/tex]

    When a=e, we get:[tex]\frac{dy}{dx}=\frac{1}{x}[/tex]. So it is just a special case of a general case.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook