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Partial derivatives of a function

  1. Oct 22, 2011 #1
    1. The problem statement, all variables and given known data

    Find the partial derivatives (1st order) of this function:

    [itex] ln((\sqrt{(x^2+y^2} - x)/(\sqrt{x^2+y^2} + x)) [/itex]

    2. Relevant equations

    3. The attempt at a solution

    I obviously separated the logarithm quotient into a subtraction, then applied the rule d ln(u) = 1/u. However, what I end up with is four terms with a bunch of x²+y² and [itex]\sqrt{x²+y²} [/itex] . I'm just starting out with partial derivatives so is there any obvious trick that I'm not familiar with in this type of situation?
    Last edited: Oct 22, 2011
  2. jcsd
  3. Oct 22, 2011 #2
    You were on the right track.
    [itex] ln((\sqrt{(x^2+y^2} - x))-ln((\sqrt{x^2+y^2} + x)) [/itex]
    You can now take the partial derivative of this function with respect to x, then respect to y.

    [tex]\frac{\partial ln[f(x, y)]}{\partial x}=\frac{1}{f(x, y)}\frac{\partial f(x, y)}{\partial x}[/tex]
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