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Sticky differentiation

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data
    I am trying to differentiate log((x+(x^2+y^2)^0.5)/(-x+(x^2+y^2)^0.5)) with respect to y

    2. Relevant equations

    I know that d/dx of ln(x) = 1/x but i am getting really confused when it comes to differentiating wrt to y?

    Can I have some help please!

    3. The attempt at a solution
  2. jcsd
  3. Feb 23, 2009 #2


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    Homework Helper

    Use the chain rule

    [tex]\frac{d}{dy}= \frac{dx}{dy}*\frac{d}{dx}[/tex]

    So if you had to differentiate ln(x) w.r.t y

    [tex]\frac{d}{dy}(lnx)= \frac{dx}{dy}*\frac{d}{dx}(lnx) = \frac{1}{x}*\frac{dx}{dy}[/tex]
  4. Feb 23, 2009 #3


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    Gold Member

    The argument is [tex]\frac{x+\sqrt{x^2+y^2}}{-x+\sqrt{x^2+y^2}}[/tex]

    So when differentiating with respect to y it looks like [tex]\frac{a+\sqrt{a+y^2}}{-a+\sqrt{a+y^2}}[/tex]

    where x is just treated as some constant a

    So you just use the chain rule for that derivative

    Does that look a little less confusing?
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