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

Hard to slove

  1. Feb 18, 2007 #1
    Who can slove this one:

    f(x) = [ln(x) {{1-e^(3x)}^3}] / [{1+e^(3x)}^3x]

    f '(x) = ¿¿¿¿??????? :surprised :surprised :surprised :surprised
     
  2. jcsd
  3. Feb 18, 2007 #2

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    Again, please show your work for this homework question. What methods of differentiation do you know of?
     
  4. Feb 18, 2007 #3
    alba_ei,

    This is not difficult but a little bit long to write.
    What is your objective?
    Is it for some homework, or do you have a practical application?

    For an homework, the result would not be helpful for you, only the method matters.
    There are only known functions in this expression: products, divisions, logarithm, exponential.
    Reading a table of derivatives rules and a bit of patience is enough.
    On wiki you can find the basis about derivatives and the http://en.wikipedia.org/wiki/Derivative" [Broken].

    For a practical application, more details would be needed to decide how to proceed for the best result.
    If this derivative is the only one in the project, then using a software like Mathematica could avoid any typing error.
    If you only need numerical results, then "Numerical Recipes" explains what to care for.

    Michel
     
    Last edited by a moderator: May 2, 2017
  5. Feb 18, 2007 #4
    alba_ei,

    As lalbatros suggests, this may be long and messy. But consider breaking this down into managable parts. For example, let your function be

    f(x) = ln(x)*R(x)

    where R(x) = P(x)/Q(x)

    Then, apply the various rules of differentiation (product, quotient, etc) to perform the derivative. Start simply, and break each component down.

    For example, start with

    f'(x) = [ln(x)]' * R(x) + ln(x) *R'(x)

    In the end, you should be able to find an expression for f'(x) in the form

    f'(x) = R(x) * W(x)

    where W(x) = 1/x + ln(x) * s(x) (you find s(x))

    Give it a try, and come back if you still get stuck.
     
  6. Feb 18, 2007 #5
    well, I saw that derivate on some past exam so the last night I remmember it and post it, just for curiosity because I can't slove it.

    f(x) = ln(x)*R(x)

    where R(x) = P(x)/Q(x)

    I get stuck when I try to get the derivate of R(x).
     
  7. Feb 18, 2007 #6

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    Use the quotient rule: [tex]R'(x)=\frac{Q(x)P'(x)-P(x)Q'(x)}{Q(x)^2}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Hard slove Date
Hard Integral Question Jan 13, 2016
Trouble with basic algebra in Calculus 1. Sep 23, 2015
Hard Integration May 4, 2015
Hard integrals in 2D Oct 17, 2014