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Natural log (ln x) derivative question

  1. Jan 2, 2013 #1
    1. The problem statement, all variables and given/known data

    This is to help out a 40something calc student -- thank you all in advance for your help

    2. Relevant equations

    If f (y) = ln ln ln x, what is ∂y/∂x?

    3. The attempt at a solution

    I came up with 1/x, which I got by applying ∂y/∂x ln x = 1/x three times, is this right? Thank you again for your help.
  2. jcsd
  3. Jan 2, 2013 #2
    Is that a ##f(y)##? Or like ##f(x) = y =~ ...##
  4. Jan 2, 2013 #3
    I might have used the terminology incorrectly --

    y = ln ln ln x

    What is y prime?
  5. Jan 2, 2013 #4


    Staff: Mentor

    As BloodyFrozen already noted, that should be f(x) = ...

    Also, the problem should be asking for dy/dx, not ∂y/∂x, which is the partial derivative of y with respect to x. Unless I'm missing something, you want the ordinary derivative, dy/dx.
    No, it's not right. You have a composite function, y = ln(ln(ln(x))), so you need to use the chain rule a couple of times. It also might be helpful to include parentheses as I did.

    In response to your other question, you can take y' to be a synonym of dy/dx.
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