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Homework Help: How to solve this logarithmic function?

  1. Nov 20, 2012 #1
    How do I find the derivative of (x)=ln(x+(x^2-1)1/2)

    The answer is suppose to be 1/(x2-1). But I keep ending up with 2x/(x2-1).
     
    Last edited: Nov 20, 2012
  2. jcsd
  3. Nov 20, 2012 #2

    Mark44

    Staff: Mentor

    Is this supposed to be f(x) = ...
    Show us what you did.

    Also, do not delete the three parts of the homework template. They are there for a reason.
     
  4. Nov 20, 2012 #3
    Well, the problem says h(x).


    (d/dx)ln(x+(x2-1)1/2*(d/dx)(x+(x2-1)1/2*(d/dx)(x2-1)1/2*(d/dx)(x2-1).

    1/(x+(x2-1)1/2 * 1+[x/(x2-1)]1/2 * x/(x2-1)1/2 * 2x

    Which actually gets me 2x2/(x2-1)
     
  5. Nov 20, 2012 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I can't decipher that line. Left and right parentheses don't match up. Is there an equals sign missing? If not, I don't understand why there are any log terms in there.
     
  6. Nov 20, 2012 #5

    Mark44

    Staff: Mentor

    How was I to tell? You wrote this
    There are actually too many "d/dx" operators in there, although I get what you're trying to do. Your task is to do this differentiation:

    d/dx(ln(x+(x2-1)1/2)

    $$= \frac{1}{x + (x^2 - 1)^{1/2}} \cdot d/dx(x + (x^2 - 1)^{1/2})$$
    $$= \frac{1}{x + (x^2 - 1)^{1/2}} \cdot (1 + d/dx[(x^2 - 1)^{1/2}]$$
    and so on, whittling away at it a little at a time.
     
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