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: Finding the nth derivative

  1. Sep 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the formula for the nth derivative of the equation f(x)= 1/(1-x)^2

    2. Relevant equations

    3. The attempt at a solution
    I have no idea how to attempt this problem. I've tried finding derivatives in order to find a pattern but I can't seem to come up with a pattern that would help me to find a formula
  2. jcsd
  3. Sep 30, 2007 #2


    User Avatar
    Homework Helper

    Let's start by listing the derivatives you've found. To make this easier to deal with, you could write the function as

    f(x) = (1-x)^(-2) and use the Chain Rule. What is f'(x)?
  4. Sep 30, 2007 #3
  5. Sep 30, 2007 #4
    Can you write that in terms of the original f? Does that help when you apply the derivatives again?
  6. Sep 30, 2007 #5
    By finding up to the fourth derivative I came up with this formula:

    nth deriv of f= (n+1)(n!)(1-x)^-(n+2)
  7. Sep 30, 2007 #6


    User Avatar
    Homework Helper

    Yes! (I had to revise something I was going to say: the (-1) factor from the Chain Rule keeps canceling the minus sign from the exponent-factor, so this does stay positive.)

    The one further simplification you can make is that (n+1) ยท (n!) = (n+1)!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook