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!

Homework Help: How can one find the dervative of a function

  1. Oct 14, 2008 #1
    How can I find the derivative of a function say, f(n) = ln(n), where n is a natural number?

    In other words, how can find g(x) in the following equation:
    f(x) + g(x) = f(x+1)

    I know there isn't a general formula for this, but are there some techniques to find g(x) for a specific equation f(x)?
  2. jcsd
  3. Oct 14, 2008 #2


    User Avatar
    Science Advisor

    If you mean the domain of f is the set of natural numbers, then there is no derivative. The domain has to be a continuous set in order to define a derivative.

    As far as finding g(x) in f(x)+ g(x)= f(x+1) is concerned, what's wrong with the obvious g(x)= f(x+1)- f(x)? Unless you have more information on f(x) I don't know what else you want.

    Are you, perhaps, talking about "finite differences"? The finite difference [itex]\Delta f[/itex] is defined as f(n+1)- f(n) for functions defined only on the natural numbers or, more generally, as (f(x+h)- f(x))/h for h a fixed, non-zero, real number. Still the only way to calculste f(n+1)- f(n) is to evaluate f(n+1) and f(n) and actually do that algebra.
    Last edited by a moderator: Oct 15, 2008
  4. Oct 16, 2008 #3
    I guess technically I was talking about "finite differences," but I wanted to find it in terms of the actual derivative of the function. Here's an easy example:

    f(n) = n^2, n ∈ ℕ

    The finite difference here is expressed through the derivative of the function. I realize that this would readily cancel out, just like f(n) - f(n) + f(n+1) = f(n+1) would, as it would with most polynomial functions, but I'm wondering that for a function like ln(n), there exists the finite difference in terms of f'(n) where it wouldn't readily cancel out.

    If we take for example, f(n) = ln(n), a simple guess could be made about the finite difference in terms of f'(n):


    though probably not true.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook