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Help me solving a Derivation equation

  1. Mar 8, 2014 #1
    1. The problem statement, all variables and given/known data
    find the derivative of the given function:

    f(x)= 6 - (1/x) / x-2

    2. Relevant equations

    3. The attempt at a solution
    the solution on the answer key is (-6x^2 + 2x - 2 ) / (x^2 (x-2)^2)

    i don't know how to solve it :(
  2. jcsd
  3. Mar 8, 2014 #2

    Simon Bridge

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    Welcome to PF;
    Lets just check that I understand you:

    You are given $$f(x)=\frac{6-\frac{1}{x}}{x-2}$$... and you are asked to find $$f^\prime (x)=\cdots$$

    It looks awkward - have you tried expressing the fraction in a simpler form?
    There is a rule for differentiations where f(x) takes the form: $$f(x)=\frac{g(x)}{h(x)}$$ ... do you know what that is?
  4. Mar 8, 2014 #3


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    Assuming that Simon correctly interpreted what your function should have actually been, you needed to include sufficient parentheses .

    f(x) = (6 - (1/x) ) / (x-2)
    Last edited: Mar 8, 2014
  5. Mar 8, 2014 #4

    Ray Vickson

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    You have written
    [tex] f(x) = 6 - \frac{1}{x x} - 2 = 4 - \frac{1}{x^2}[/tex]
    This is what I get when I read your expression using standard parsing rules for mathematical expressions.
    If you mean hte above then you do not need to change anything. However, if you mean
    [tex]f(x) = 6 - \frac{1}{x(x-2)}[/tex]
    then you need parentheses, like this: f(x) = 6 - 1/(x(x-2)). If you mean
    [tex] f(x) = \frac{6 - (1/x)}{x} - 2[/tex]
    then you need parentheses, like this: f(x) = (6 - (1/x))/x - 2. Finally, if you mean
    [tex] f(x) = \frac{6 - (1/x)}{x-2}[/tex]
    then use parentheses like this: f(x) = (6 - (1/x))/(x-2).
  6. Mar 8, 2014 #5

    Simon Bridge

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    Well, considering that: $$\frac{d}{dx}\frac{6-\frac{1}{x}}{x-2}= \frac{-6x^2 + 2x - 2}{x^2(x-2)^2}$$... it's probably a good guess ;)

    What is needed now is a follow up from you.
    It is tricky to guide you through this one without effectively providing the answer so I want to know where you are stuck. Please show us your best attempt.
  7. Mar 9, 2014 #6


    Staff: Mentor

    Please, no more help, hints, or guidance until ishahad returns.
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