Finding the nth derivative

  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. dynamicsolo

    dynamicsolo 1,662
    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. f'(x)=2(1-x)^-3
     
  5. Can you write that in terms of the original f? Does that help when you apply the derivatives again?
     
  6. 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. dynamicsolo

    dynamicsolo 1,662
    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)!
     
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