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Simplify and find derivative

  1. Jul 24, 2012 #1
    question is...

    (ln(2x+1/(1-x)-4x+x/(1-x)+2x))/2

    I start by simplifying and then finding the derivative...correct?
     
  2. jcsd
  3. Jul 24, 2012 #2
    That's what I would do.
     
  4. Jul 24, 2012 #3
    (1-x)s factor? Any tips on a start, self teaching calculus is difficult
     
  5. Jul 24, 2012 #4

    Mark44

    Staff: Mentor

    What are you asking?
    Just so we're all starting on the right page, is this what you're working with, as what you're taking the natural log of?

    $$2x + \frac{1}{1 - x} - 4x + \frac{x}{1 - x} + 2x $$


    What you wrote is (1/2)ln(y), with y being the expression above.
     
  6. Jul 24, 2012 #5
    Simplifying gives you a simple log to derive.
    Recall that division inside of logs means subtraction of top and bottom.
    That should give you a simpler derivative to take in my opinion.
     
  7. Jul 24, 2012 #6
    I am just looking for help on how to solve the problem.
     
  8. Jul 24, 2012 #7
    I don't think anymore help can be given without giving the answer away.
     
  9. Jul 24, 2012 #8
    ok, ill solve it. Hopefully someone will verify the answer I find and let me know if I am right
     
  10. Jul 24, 2012 #9
    2
    (1-x)^2 - 2
     
  11. Jul 24, 2012 #10

    eumyang

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    Homework Helper

    You should learn to use LaTeX. Is the above supposed to be this?
    [tex]\frac{2}{(1 - x)^2 - 2}[/tex]
     
  12. Jul 24, 2012 #11
    The denominator is ((1-x)^2-2)
    =x^2-2x-1
    correct?
    If so, try re-checking your algebra.
     
  13. Jul 24, 2012 #12

    Mark44

    Staff: Mentor

    I don't think that's right, but I'm not sure what the problem is, since you didn't answer the question I asked in post #4.

    The title of your post is "Simplify and find derivative" so I assume that the problem is to simplify the expression and then take its derivative.

    What do you get when you simplify the expression, before you take its derivative?
     
  14. Jul 24, 2012 #13
    2(x^2-2x+2)/(1-x)
     
  15. Jul 24, 2012 #14
    i am looking into LaTex, I apologize for my mathematical formatting computer skills
     
  16. Jul 24, 2012 #15
    This is quite vague, is that the simplification?
    If the inside of your log looks like what what mark posted, then the 2x, 2x, and 4x, all cancel out.
    The last remaining terms have common denominators so you can add them.
     
  17. Jul 24, 2012 #16

    micromass

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  18. Jul 24, 2012 #17
    -2x+2+2/(1-x)

    derivative = -2 + 2/(1-x)^2

    I am driving many of you nuts and I thank you for your patience
     
  19. Jul 24, 2012 #18
    Derivative of that is correct, but isn't it inside of a natural log, and according to the original equation that was given, the simplification would be
    ln((1+x)/(1-x))
     
  20. Jul 24, 2012 #19
  21. Jul 24, 2012 #20

    eumyang

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    Homework Helper

    Yes, you are driving us nuts, because you are not being clear in who you are replying to (or you do not completely answer someone's question), and because you show only snippets of work, not the whole thing.

    First thing (and Mark44 asked this already), is this what is supposed to be inside the natural log? Yes or no?
    [itex]2x + \frac{1}{1 - x} - 4x + \frac{x}{1 - x} + 2x [/itex]

    Second, where did the bolded come from?
    If the bolded is supposed to be a simplification of the LaTeX I wrote above, then it's wrong. Show us all of your work. Be clear and precise. Otherwise, people won't want to help you.
     
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