1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Interpretation of f'(x)/f(x)

  1. Jan 24, 2016 #1
    Hi! I'd like to know of f'(x)/f(x) has some special interpretation, some physic or math concept related.

    This ratio appears many times in control theory...
  2. jcsd
  3. Jan 24, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Hehe, no idea. However, the inverse is where a linear approximation to f crosses the y-axis.
    See also Newton-Raphson
  4. Jan 24, 2016 #3


    User Avatar
    2017 Award

    Staff: Mentor

    Since its anti-derivative is ##ln|f(x)|## it's natural to often occur everywhere. However, that doesn't justify a special name. E.g. ##e^{- \frac{1}{2} x^2}## hasn't either.
  5. Jan 25, 2016 #4


    User Avatar
    Gold Member

    It is the derivative of ##\log{(f)}##, ##\log##-transformations are used when there are quantities with exponential growth as in biology, control theory, in information theory as example ##\log{f}## is connected to the concept of entropy, ...
  6. Jan 25, 2016 #5


    User Avatar
    Science Advisor

    In complex analysis, if f(z) is a meromorphic function inside and on some closed contour C, and f has no zeros or poles on C, then
    where N and P denote respectively the number of zeros and poles of f(z) inside the contour C, with each zero and pole counted as many times as its multiplicity and order, respectively, indicate. This statement of the theorem assumes that the contour C is simple, that is, without self-intersections, and that it is oriented counter-clockwise (see https://en.wikipedia.org/wiki/Argument_principle).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook