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Instances where Logarithmic Differentiation doesn't work?

  1. Oct 14, 2015 #1

    In my class we just learned about logarithmic differentiation. I can see this being useful when taking the derivative of a complex function since it could be messy. But, I tried it on simpler equations as well. Everything I tried it on it seemed to work. Are there ever instances that it does not work?

    To make sure we are using the same definition of logarithmic differentiation, I simply mean taking the log of both sides of an equation before taking its derivative. So where:

    y = x2
    ln y = ln (x2)
    1 / y * y' = 1 / x2 * 2x
    y' = 2y / x
    y' = 2x

    Certainly just taking the derivative of this is easier, but it's just an example.
  2. jcsd
  3. Oct 14, 2015 #2


    Staff: Mentor

    To the best of my knowledge, no.
    Your example is a very simple one, for which log differentiation is a lot more work than it would be by simpler means.

    Here are some examples where log differentiation would be very useful.
    1. ##y = (3x^2 + 5)^{1/x}##
    2. ##y = (\sin x)^{x^3}##
    (from https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/LogDiff.html)
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