1. Not finding help here? Sign up for a free 30min 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!

Finding the nth derivative of a function

  1. Jan 22, 2017 #1
    1. The problem statement, all variables and given/known data
    I'm trying to find a formula for the nth derivative for the function f(x)=x1/3

    3. The attempt at a solution
    I know that it has alternating signs so it start with (-1)n+1 and I know the exponent for it is x(1/3-n) but I'm having a hard time figuring out the coefficient of x.

    For the fourth derivative I have 1/3(1/3-1)(1/3-2)(1/3-3)x(1/3-4)


    The example our teacher gave us was x-1 which was much easier in my opinion...
     
  2. jcsd
  3. Jan 22, 2017 #2
    Try expressing the powers and the coefficients in a fractional form while taking derivatives and see if the pattern becomes clearer that way.
     
  4. Jan 22, 2017 #3
    I rewrote it three different ways and I'm still having a hard time seeing the complete pattern.

    I'm using the fourth derivative: f4(x)=(1/3)(-2/3)(-5/3)(-8/3)x-11/3
    and: f4(x)=(1/3)(1/3-1)(1/3-2)(1/3-3)x-11/3
    and:f4(x)=(1/3)(1/3-3/3)(1/3-6/3)(1/3-9/3)x-11/3

    So far I have fn(x)=(-1)n+1(?/3n)x1/3-n
     
  5. Jan 22, 2017 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    IMHO it is much easier to work with the general form ##f(x) = x^p##, then take ##p = 1/3## after all the work is finished.

    The reason it is easier is that you have symbolic factors such as ##p - 1##, ##p-2,## etc. and by keeping them symbolic you can keep straight the different "effects". For example, if you see a number like ##-2## somewhere in your calculation, it is not easy to know if it really is a ##``-2"## or a ##``-1 - 3/3"## or ##``-6/3"##---and sometimes that matters a lot when you want to look at more terms, etc. By keeping everything in terms of ##p## there is never any chance of confusion.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the nth derivative of a function
  1. Find the nth derivative? (Replies: 20)

Loading...