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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


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

    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.

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

    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


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    Use the quotient rule: [tex]R'(x)=\frac{Q(x)P'(x)-P(x)Q'(x)}{Q(x)^2}[/tex]
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