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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


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    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


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    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) · (n!) = (n+1)!
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